ACE Advanced Collapsed cone Engine

Transcription

1 White Paper ACE Advanced Collapsed cone Engine Authors: Bob van Veelen 1,Yunzhi Ma 2,3 and Luc Beaulieu 2,3 1. Elekta 2. Département de physique, de génie physique et d optique et Centre de recherche sur le cancer, Université Laval, Québec, Canada 3. Département de radio-oncologie et CRCHU de Québec, CHU de Québec, Québec, Canada

2 Contents 1. Introduction 3 2. The rationale for using ACE 3 3. Implementation of ACE in Oncentra Brachy Algorithm description and usage Algorithm configuration Dose calculations Dose normalization Comparisons Level one comparisons Level two comparisons Prostate HDR implant Breast HDR brachytherapy case Chest wall Shielded applicators Calculation time Conclusions Definition of terminology References 16 2

3 1. Introduction This white paper describes the implementation of ACE: Advanced Collapsed cone Engine in Oncentra Brachy treatment planning software, as well as the advantages of using this new paradigm for dose calculation. ACE provides the following benefits: Obtain better insight on actual dose distribution by performing more accurate dose calculations Similar accuracy to Monte Carlo dose calculation with shorter calculation times Fully integrated in Oncentra Brachy, ensuring smooth and intuitive system operation and easy integration in your current workflow For many years, no patient-specific tissue information has been accounted for in dose calculation for brachytherapy. This was due to the complexity and required calculation times that would make it unusable in daily clinical routine. Nowadays, thanks to technological advancement, more accurate dose calculation is within reach, enabling more precise dose planning and treatment customization to specific patient cases. With this paper you will: Understand what ACE is providing, in comparison to current clinical practice Obtain a dosimetric comparison of ACE to Monte Carlo dose calculations Appreciate how this new paradigm works in your treatment planning system Discover how easy it is to adopt this new dose calculation method Develop a deeper knowledge of the physics behind this algorithm 2. The rationale for using ACE The AAPM Task Group 43 has published reports describing a dose calculation formalism that is based on the assumption of a single source in the center of a large water phantom 10. This formalism is currently used as the clinical workhorse in brachytherapy. The primary reasons for this are ease of use and the calculation time required to obtain a dose distribution (see Table 1). The TG-43 dose calculation formalism does not account for any tissue heterogeneity within the patient s body or the absence of tissue outside of the body. In addition, the effects of applicator materials and shielding are also not described by this formalism, although the latter is typically accounted for in current treatment planning systems. Taking these kinds of effects into account can result in changes of up to 5% in currently accepted clinical dose parameters 9,12. Performing more accurate dose calculations to obtain a closer-to-reality view of the dose distribution inside the patient is therefore desirable. The AAPM Task Group 186 published a report 4 that is aimed at guiding early adopters of Model Based Dose Calculation Algorithms (MBDCA). 3

4 TG-43 Oncentra Brachy ACE... Monte Carlo Figure 1: Dose distribution comparison of TG-43, ACE and Monte Carlo. Dose calculation method Uses patient information Calculation speed Clinical accuracy Suited for clinical use TG-43 No < 1 sec Low - Moderate Yes Monte Carlo Yes Minutes - hours High ACE Yes 5-10 min Moderate - High No, too slow in most situations Yes, after clinical evidence collected Table 1: List of different types of dose calculation methods and their characteristics. 3. Implementation of ACE in Oncentra Brachy The additional actions that need to be performed to use ACE within Oncentra Brachy are: 1. Assign materials to the contoured regions of interest (ROIs) of the patient 2. Choose a method by which Oncentra Brachy will determine the mass density for these ROIs (uniform or image based) 3. Choose the desired accuracy level of the ACE calculation The following section gives a high-level overview of the algorithm, the input that is needed to perform the calculations and at which point the additional steps need to be performed to ensure a proper performance of ACE. 3.1 Algorithm description and usage The amount of physics that is explicitly modeled in different types of dose calculations ranges from no physics at all to practically all physics for TG-43 dose calculations and Monte Carlo dose calculations, respectively. Somewhere in between these two types of dose calculation lies ACE, which is a superposition/convolution method (see Reference 1 and Table 1). 4

5 The dose that is calculated with ACE 1,2 is determined as a sum from several components: D= Dprim + D1sc + Dmsc (1) in which D prim is the dose from the primary photons, D 1sc is the dose from once scattered photons, and D msc is the dose from all higher order scattered photons. The calculations are performed sequentially, in which dose from lower scatter order photons are used to represent the fluence for higher order dose calculations. The manner in which the scatter order separation is done is detailed in a publication from Mackie et al 8. The algorithm naturally yields Dm,m, which is the dose to the local medium of the radiation transported through the medium. Reporting this dose is also recommended by the TG-186 publication Algorithm configuration Before the actual dose calculation can be started, the input parameters for the algorithm need to be defined. There are two main choices that need to be made. The first is the number of transport directions that will be used for the first scatter dose and multiple scatter dose calculations. The second is the definition of the medium in which the calculations will take place (e.g., building a calculation volume). The first is done fully automatically and needs no user interaction, while the latter requires some actions from the user, as will be described below. Accuracy level Two distinct accuracy levels have been defined for ACE: Standard and High. The first represents a setting with which dose distributions can be calculated relatively quickly and are of a clinically acceptable quality. The latter improves the accuracy of the dose calculation, yielding dose distributions similar to that of Monte Carlo calculations. Inevitably, the High accuracy level will also increase computing time. Transport directions While the primary dose calculations are performed by a ray tracing algorithm, the scatter dose is calculated with the collapsed cone superposition convolution method. To perform these calculations the algorithm needs transport directions along which it can redistribute scattered energy. The transport directions themselves are created by a spherical tessellation, which is done while ensuring that each transport direction has approximately the same opening angle. By choosing different levels of refinement of this tessellation, a set with a different number of transport directions can be generated (see Figure 2). Figure 2: Example of a spherical tessellation. The number of transport directions for the scatter dose calculations has been made dependent on the number of dwell positions in the treatment plan. Based on a study from Carlsson Tedgren et al 3, in Oncentra Brachy default values have been chosen for the two accuracy levels (see Table 2). The two numbers in each entry of Table 2 represent the number of first scatter and residual scatter transport directions. The number of dwell positions in the plan poses several boundaries. The number of transport directions decreases when the plan exceeds a certain boundary. A special case was defined for a single dwell position with a High accuracy setting. This special case allows for a better level 1 commissioning of the algorithm as defined by the guidelines in the TG-186 publication 4. (1) Standard accuracy calculation mode 5

6 Accuracy level 1 dwell position Number of transport directions for first and residual scatter dose calculations 2-50 dwell positions dwell positions dwell positions >300 dwell positions Standard 320 and and and and and 72 High 1620 and and and and and 128 Table 2: Number of first scatter and residual scatter transport directions for the two ACE accuracy levels. Building a calculation volume The calculation volume contains the definition of the medium (densities / attenuation coefficients / energy absorption coefficients) in which the calculations take place. The input that is needed to define the medium includes: The bounding box of the primary image data set in the current case (this can be from a specific image modality, but also from an empty image series) The location of the active dwell positions (within this bounding box) The geometry and location of an applicator (optional) The contoured organs / ROIs (optional) Based on the location of the active dwell positions, a bounding box that contains all of these positions is determined. Depending on the specific accuracy level, a margin d in all directions surrounding this bounding box is added (see Figure 3). Based on the box that has been created in this way, three more boxes are created, each with an increasing margin, to obtain four boxes in total (see Figure 4 and Table 3). Regardless of the accuracy level that has been set, the voxel sizes that will be used within each of these boxes is 1, 2, 5 and 10 mm, respectively. After all four boxes (or detail levels) have been created by this method, the obtained boxes are clipped against the bounding box that is set by the image data in the current case. When required, boxes are automatically removed or expanded to gain calculation speed or accuracy. This can result in a set of margins and resolutions that deviates from the default values. Table 3 shows the default margins that are used for a given resolution and accuracy level. Figure 3: Initialization of the calculation volumes in which the implant box with the active dwell positions is expanded by a margin Δd in all directions. 6

7 Figure 4: Multiple overlapping boxes with different voxel sizes. Each box depicts a detail level in which a calculation will take place. As an example for deviations from the default values, consider a situation in which the image volume falls completely within the 20 cm margin around the dwell positions in a calculation with a standard accuracy setting. In such a situation, having an additional calculation volume (with a margin up to 50 cm) has no added benefit, since no additional information will be gained by calculating in the largest and coarsest grid. The dose calculations will not be performed in the largest box, thereby gaining some calculation speed. In addition, when the largest box provides only a marginal (<20%) amount of additional volume in which dose calculations can take place, it will also be removed and the margin of the next detail level will be extended to ensure that the entire image volume is covered, but now with a finer grid. Accuracy Level Voxel size (cm) Standard High High (single dwell position) Table 3: Margins to define the bounding boxes with different voxel sizes for different accuracy levels. Margins are given in cm. After defining the different calculation volumes, the material information for each voxel in each volume needs to be set, based on the image data, the ROI and optionally the applicator. Medium definition For the definition of the medium, two parameters are needed at all locations in the calculation volume. The first is the chemical composition of the material and the second is the mass density. For this purpose, a list of known material is compiled, which is based on table III of the AAPM TG-186 recommendations 4, with addition of the materials used in applicators and some phantom materials. Interaction coefficients On the basis of the chemical composition of the aforementioned list, the interaction coefficients are determined. These interaction coefficients are then used during the dose calculations as detailed on the next page. During the determination of the interaction coefficients, both the relative mass fraction of each type of atom in a material and the spectrum of the source are accounted for. Mass density The mass density of an ROI can be set by the user as being uniform according to table III of of the AAPM TG-186 7

8 recommendations 4. However, when a CT image data set is being used, the Hounsfield Units (HU) can help determine the mass density heterogeneity within an ROI. ICRU reports 44 5 and 46 6 were used to obtain the electron and mass density of a set of materials. Subsequently, the corresponding Hounsfield Units in column 4 of Table 4 were calculated with the formula used in the publication from Knöös et al 7. Now, to determine the mass density of an arbitrary voxel in the image data from its HU value, a linear interpolation is done between the data in the table. If the HU is above the value for Aluminum the mass density is determined with the help of extrapolation. Material ρ ρ mass mass, H2O ρ ρ elec elec, H2O HU Air Lung (inflated) Adipose tissue Water Muscle Cartilage Cortical bone Aluminium Table 4: The material, mass density, electron density and corresponding Hounsfield Units (HU) used to determine mass density based on HU. Density values have been taken from ICRU report 44 5 and ICRU report Material assignment For each ROI that has been contoured by the user, a material can be assigned. Together with this material assignment it is possible to either choose a uniform density assignment or an HU based density assignment when CT image data is available. This means that ACE for Oncentra Brachy can be used with CT images as well as MRI, ultrasound and PET images. In case of overlapping ROIs, the user needs to assign a priority to each of the overlapping ROIs to inform the system which material assignment should be used. If the image data set also contains air regions surrounding the patient, an external patient contour should be segmented to allow ACE to assign air to these regions. The system assumes that water is present when no information is available regarding material assignment. 3.2 Dose calculations This section features a high-level view of the way the algorithm is implemented in Oncentra Brachy. The steps that are described are not visible when using ACE, but are performed once the user executes the dose calculation. The dose calculation uses a formalism in which all dose components are calculated per the radiant photon energy R leaving the source encapsulation. Calculation of primary dose The primary dose calculation starts with the determination of the primary kerma by means of a ray tracing algorithm. Since the primary kerma will also be used as the source of energy for the scatter dose calculation, it will be calculated considering volume averaging to ensure energy conservation. The volume-averaged primary kerma, Kprim, is calculated by: where is a voxel averaging factor, is a correction factor for the energy fluence and energy absorption anisotropy, a correction factor for the attenuation anisotropy, is the mass energy absorption coefficient for the medium at is the mass attenuation coefficient, is the radius from the point in which the kerma is calculated to the source dwell position, is the mass density, is the voxel size, and is the angle between the source 8

9 direction and the vector to the location where the kerma is being calculated, similar to the definition in the TG-43 formalism. The ray tracing in the exponent takes into account all materials found in its path, going from the source to the location where the primary kerma is being calculated. This is based on the materials that are found in the voxels that are crossed, but also the materials that are found through intersection calculations with the applicator, if one is present in the treatment plan. The primary dose is calculated with help of the primary kerma by: where is a correction factor that takes into account electron transport buildup, finite source length effects and ensures that the primary dose distribution close to the source is compatible with the data that were used to characterize the source. The primary kerma is also used to determine the first scatter scerma (SCattererd Energy Released per unit MAss), S1sc, by: which is used as input for the subsequent scatter dose calculations. The scerma is the part of the energy of the primary photons that did interact, but was not absorbed, and will be released as scattered energy to be redistributed in the calculation volume. Calculation of scatter dose Based on a specific set of transport directions, at the start of the calculation, a series of lattices of parallel transport lines is determined, one lattice for each transport direction. Along each line, in the series of lattices, the energy that can be extracted from the scerma is redistributed within the calculation volume. This redistribution of energy along the transport lines is the core of the algorithm and can be described with the following steps: 1. Initialize a variable, the radiant energy, to zero. 2. Take a step (voxel-by-voxel) along the current transport line and for each step determine: The amount of energy that is currently available in which can be locally deposited; The amount of energy that is locally released (due to scerma) and directly absorbed again, which will cause no change in but only to the locally deposited dose; The amount of energy that is locally released and transported away. 3. From the above three components (a-c) calculate the addition to the first scatter dose from this transport line to the voxel. Figure 5 is a graphical representation of the steps listed above. When crossing a voxel, the initial is changed by the value for that is determined to obtain at the exit of the voxel. The value of depends on the three effects mentioned under point 2 above. Performing these steps for all transport lines in all lattices and all transport directions, and summing all the additions to the first scatter dose that are given by the calculations performed, results in the first scatter dose distribution. The three different components in step 2 of the above described algorithm are based on the local conditions taken from the medium that has been defined (density, attenuation and absorption coefficients) and the point kernel parameters. These point kernel parameters have been determined in a pre-processing step with results from MC simulations. 9

10 After the first scatter dose calculation the remaining amount of energy that can be scattered onto the higher order scatter component, namely the multiple scatter dose, must be determined. This is called the multiple scatter scerma. On the basis of the multiple scatter scerma, the above mentioned algorithm is applied once more to obtain the multiple scatter dose distribution. Figure 5: The changes to the radiant energy, R, that occur when a transport line crosses a single voxel along its path during the scatter dose calculations. 3.3 Dose normalization The output of the above discussed algorithm is the value of at any location in the grid. The absolute dose rate value is then obtained by: in which is the value for the radiant energy scaled dose in a reference point when dose calculations would be performed for a single dwell position in a water phantom, and and are the usual values for the air kerma strength and the dose rate constant, similar to the TG-43 dose calculation formalism. 4 Comparisons TG-186 defines two different levels of validation of model-based dose calculation algorithms 4. In level 1, calculation should be performed in full scatter conditions, replicating TG-43 conditions. In level 2, the advanced features of the dose calculation engine should be compared against a well-validated Monte Carlo code for the same cases or to experimental measurements. 4.1 Level one comparisons Figure 6 shows an example of level 1 comparison in water and for full scatter condition between the collapsed cone convolution (CCC) ACE algorithm and TG-43. The color wash is the ratio of the dose calculated with ACE divided by the dose calculated with TG-43 in percentages. First, it can be seen that the isodose lines correspond almost perfectly between ACE and TG-43. The top left panel shows ripple in the ACE 2% isodose line. This relates perfectly to the strong ray effect seen in the color wash ratio plot. Ray effect is related to a build-up of fluence along the transport lines, when the number of transport lines is too low 2. The difference is related to the scatter components; this is why the effect increases in distance from the center (the dose in the first few cm is dominated by the primary dose which is calculated without any approximation). 10

11 Figure 6: Ratio between doses calculated by ACE and TG-43 (ACE/TG-43) for single dwell position (left) and 8 dwell positions (right) for a calculation performed in water and full scatter conditions (only the first 20 x 20 cm 2 is shown in the figure). The top panels show the dose distribution calculated with ACE standard accuracy. The bottom panels show the dose distribution calculated with ACE high accuracy. Note that the large difference seen (more than ±10%) in the upper left panel (single dwell position, standard ACE accuracy) is a local difference and located past the 2% isodose line level. Therefore, this difference has little clinical importance. When the number of dwell positions increases, there is a superposition of the transport lines from all dwell positions, which smoothed out this effect. This is clearly seen in the top right panel for the 8 dwell-positions scenario. Here, the effect is at most 3% at a distance past the 1% isodose line level. The effect of the adaptive calculation resolution (e.g. Figure 3 and Figure 4) can also been seen in the upper panels. Moreover, the isodose lines show no residual structure. This allows us to conclude that for most clinical situations, the standard resolutions will be appropriate. In the bottom panel, the calculations with ACE are now performed with high accuracy (1,620 directions). For the single dwell position, the ray effect is highly attenuated and corresponds to no more than ±5% beyond the 2% isodose line and is non-existent for the 8 dwell positions case. Dose distributions of such high resolutions can be calculated in a reasonable amount of time only for a few dwell positions (< 6-8). Although for most clinical situations the standard resolution will be appropriate, high (720 directions) or adapted high (1,620 direction) resolution is needed for basic level 1 commissioning of a few dwell positions (<5). Under these conditions, ACE performance agrees with TG-43 also for extreme calculation situations. 4.2 Level two comparisons In this section, various clinical cases will be used to compare the performance of ACE to the current clinical standard (TG-43) and also to the performance of a well-validated Monte Carlo (MC) code based on GEANT4 Algebra 11. Unless stated otherwise, calculations with ACE are performed using the standard accuracy definition and all materials are assigned based on TG-186 recommendation using organ contours and recommended uniform density. The same material assignments were used for MC calculations. 1 mm 3 voxels were used for MC and the number of photons was chosen at 1x

12 4.2.1 Prostate HDR implant This first case represents a clinical situation in which the calculation conditions are expected to be very close to TG-43 conditions. The particular case chosen is that of a 17 plastic catheter implant used to deliver a 15 Gy boost in a single fraction. The plan contains a total of 111 dwell positions. All isodose lines match between all three methods until the 50% isodose line (Figure 7). A small difference is seen between isodose lines of ACE and TG-43 in the rectum area (20% isodose lines) but this is due to setting the whole rectum volume to air to test the advanced calculation method. The largest local difference is seen at the pelvic bones, 10% isodose lines and lower. To better illustrate the differences in dose calculation of ACE, MC and TG-43, a dose profile is given in Figure 8. The dose difference between ACE and MC in the middle of the rectum (set to air) is below 3%, with MC very close to TG-43. Both advanced dose calculation algorithms differ significantly from TG-43 in the bone region as expected. ACE is unable to reproduce the full dose accumulation effect of the bone (difference of about 15% at the entrance and about 10% at the exit). Again, these differences are local dose differences of much smaller dose levels (below 1.5 Gy relative to a prescription dose of 15 Gy). Thus a 10% difference represents 0.15 Gy or less in absolute values. The reason for this discrepancy between ACE and MC dose calculation finds its origin in the pre-calculated MC kernels used by ACE for the multiple scatter components. These are generated in water. Finally, the DVHs of all regions of interests are given in Figure 11. No large discrepancies are shown for the target and organs-at-risk. Figure 7: Isodose lines for a prostate HDR case calculated with TG-43, ACE and Monte Carlo (MC). For this particular test, the rectum was set to air to maximize the difference in output of the dose calculation algorithms. The horizontal dashed line indicates where a dose profile was drawn (Figure 8). Figure 8: Dose along the dashed line represented in Figure 7, normalized to the dose calculated with TG-43 for ACE and MC Breast HDR brachytherapy case A breast balloon HDR brachytherapy case is explored next. This is an interesting case because the presence of air outside the patient, lung and balloon cavity should provide a good test for the ability of the advanced dose calculation algorithm to calculate the dose when the full scatter condition is not fulfilled. The applicator that is used is the 7 (6-1) catheters SAVI applicator with 45 active dwell positions. The calculations with ACE were performed for standard and high accuracy mode. 12

13 The overestimation of dose with TG-43 is obvious from Figure 9. TG-43 isodose lines are the most external ones in all cases, with differences already visible for the 100% isodose line and significant at the 50% isodose line level. Both standard and high accuracy modes yield the same results for the ACE algorithm, and ACE and MC isodose lines match very well within the body. There is only a small difference between the ACE and MC 10% and 20% isodose lines in air outside the body. The DVHs (Figure 11) confirms the agreement between ACE and MC, and the significant differences relative to TG-43 for the PTV. Note that the skin contours were unavailable for this case. However, the difference relative to TG-43 in the DVHs should be larger than that seen for the target, as the lack of scatter radiation will lead to a significant decrease of the skin dose calculated with ACE or MC. Figure 9: Breast balloon HDR brachytherapy case using a SAVI applicator. Here, standard and high accuracy options in ACE were compared to MC and TG-43. The 100, 50, 20 and 10% isodose lines are overlaid Chest wall An extreme case relative, to the full scatter condition of TG-43 (for a non-shielded implant at least), is a chest wall implant using 14 catheters and 344 active dwell positions (Figure 10). Heart, lung, skin and target were contoured. As in the breast SAVI case, the difference between TG-43 and the other two methods is obvious. The lack of strong scattering materials (water) results in a faster dose absorption with distance and compresses the isodose lines calculated with the advanced methods. The agreement between the dose distributions of ACE (CCC) and MC is excellent. The only small difference is seen in the 10% isodose lines. The DVHs (Figure 11) confirm the good agreement between ACE and MC. TG-43 overestimates the dose for all contoured structures. Figure 10: Chest wall implant. Standard accuracy ACE (CCC) calculation is compared to MC and TG-43. The 100, 90, 50, 20 and 10% isodose lines are overlaid. 13

14 Figure 11: DVH curves for the prostate, chest wall and breast implants shown in figures 7, 10 and 9, respectively Shielded applicators While the above sections look at the differences due to tissue heterogeneities and lack of scatter medium, here we briefly discuss the effects due to shielding. Accounting for the effects of shielding on the dose distribution can be done by using the Applicator Library for Oncentra Brachy. By placing an ACE supported applicator into the treatment plan, the geometry and location of the applicator and all applicator materials are automatically taken into account by the dose calculations. Figure 12 shows a comparison between the dose distributions calculated with TG-43 and ACE for the Fletcher CT/MR Shielded applicator. The figure shows both dose distributions and the corresponding DVH curves. Further information regarding this applicator and its use in combination with ACE can be found in White paper Fletcher CT/MR Shielded applicator with ACE (document number MKT). Figure 12: Comparison of dose distributions calculated with TG-43 and ACE. Top left: TG-43 dose distribution. Top right: ACE dose distribution. Bottom: Comparison of DVH curves for the two dose distributions Calculation time For most clinically relevant HDR implants, calculation time will be less than 10 minutes using the standard accuracy setting. This includes most applicator-based GYN, esophagus and breast implants. The latter two with any superficial brachytherapy geometries and shielded applicators (GYN and rectum) will benefit most from using the ACE algorithm, compared to using the standard TG-43 algorithm. It is important to remind that at this time, the societal 14

15 recommendation 4 is to continue to use TG-43 for dose prescription levels and for dose optimization. ACE should be used in parallel to TG-43 for dose recalculation only. Case Catheters Dwell positions Standard ACE run-time (min) High High (single dwell position) All-water case - 1 <1 1 4 All-water case Breast (SAVI) Prostate Chest wall Table 5: Calculation times for all cases presented in this section. 5 Conclusions In this white paper we have illustrated for which clinical cases it is beneficial to use ACE for more advanced and detailed dose calculations. We have given a rationale for using more advanced dose calculations in general and discussed details regarding the ACE implementation in Oncentra Brachy. By performing a comparison between the results of ACE and the gold standard Monte Carlo dose calculations, we have shown that for the most common clinical cases, the results of ACE and Monte Carlo are in good agreement. When the number of dwell positions are above 6-8, the Standard accuracy setting in ACE leads to overall results in terms of isodose lines and DVHs that are on par with the High accuracy setting in ACE. For TG-186 level 1 commissioning, when using a water phantom, an adapted high accuracy mode is needed for a single dwell position to achieve results comparable with TG-43. Comparisons at doses lower than the 1-2% isodose level will, however, show local dose discrepancies and this is consistent with the ACE implementation. Due to the low dose level, these differences are clinically irrelevant. Some limitations remain around high-z materials and other circumstances. They are related to the pre-calculated kernels used for the scatter components. These effects will be minimal in the first few centimeters where the primary dose dominates. ACE: Advanced Collapsed cone Engine and all its advantages is available in the new version of Oncentra Brachy (from version 4.4). 6 Definition of terminology Abbreviation / definition ACE CCC MC MBDCA ROI DVH HDR HU SAVI AAPM ICRU Description Advanced Collapsed cone Engine Collapsed Cone Convolution Monte Carlo Model Based Dose Calculation Algorithm Region of Interest Dose Volume Histogram High Dose Rate Hounsfield Units TG-43 Task Group 43 Strut Adjusted Volume Implant TG-186 Task Group 186 American Association of Physicists in Medicine International Commission on Radiation Units & Measurements 15

16 7. References [1] Ahnesjö A (1989). Collapsed cone convolution of radiant energy for photon dose calculation in heterogeneous media. Med. Phys. 16 pp [2] Carlsson ÅK, Ahnesjö A (2000a). The collapsed cone superposition algorithm applied to scatter dose calculations in brachytherapy. Med. Phys. 27 pp [3] Carlsson Tedgren Å, Ahnesjö A (2008). Optimization of the computational efficiency of a 3D, collaped cone dose calculation algorithm for brachytherapy. Med. Phys. 35 pp [4] Beaulieu L, Carlsson Tedgren A, Carrier J-F, Davis S D, Mourtada F, Rivard M J, Thomson R M, Verhaegen F, Wareing T A, Williamson J F (2012). Report of the Task Group 186 on model-based dose calculation methods in brachytherapy beyond the TG-43 formalism: Current status and recommendations for clinical implementation, Med. Phys. 39, pp [5] International Commission on Radiation Units and Measurements (1989). Tissue substitutes in radiation dosimetry and measurement. ICRU 44. [6] International Commission on Radiation Units and Measurements (1992). Photon, electron, proton & neutron interaction data for body tissues. ICRU 46. [7] Knöös T, Nilsson M, Ahlgren L (1986). A method for conversion of Hounsfield number to electron density and prediction of macroscopic pair production cross-section. Radiother. Oncol. 5 pp [8] Mackie TR, Bielajew AF, Rogers DWO, Battista JJ (1988). Generation of photon energy deposition kernels using the EGS Monte Carlo code. Phys. Med. Biol., Vol. 33, No 1, [9] Rivard MJ, Venselaar JLM, Beaulieu L (2009). The evolution of brachytherapy treatment planning. Med. Phys. 36, pp [10] Rivard MJ, Coursey BM, DeWerd LA, Hanson WF, Huq MS, Ibbott GS, Mitch MG, Nath R, Williamson JF. (2004). Update of AAPM task group no. 43 report: a revised AAPM protocol for brachytherapy dose calculations. Med. Phys. 31 pp [11] Afsharpour H, Landry G, D Amours M, Enger S, Reniers B, Poon E, Carrier JF, Verhaegen F, Beaulieu L (2012). ALGEBRA: Algorithm for the heterogeneous dosimetry based on GEANT4 for BRAchytherapy. Phys. Med. Biol., Vol 57, No 11, [12] Ma Y, Lacroix F, Lavallee M-C, Beaulieu, L, Validation of the Oncentra Brachy Advanced Collapsed cone Engine for a commercial 192 Ir source using heterogeneous geometries, Brachytherapy (2015), org/ /j.brachy About Elekta Elekta s purpose is to invent and develop effective solutions for the treatment of cancer and brain disorders. Our goal is to help our customers deliver the best care for every patient. Our oncology and neurosurgery tools and treatment planning systems are used in more than 6,000 hospitals worldwide. They help treat over 100,000 patients every day.the company was founded in 1974 by Professor Lars Leksell, a physician. Today, with its headquarters in Stockholm, Sweden, Elekta employs around 4,000 people in more than 30 offices across 24 countries. The company is listed on NASDAQ OMX Stockholm. Corporate Head Office: Elekta AB (publ) Box 7593, SE Stockholm, Sweden Tel Fax info@elekta.com Regional Sales, Marketing and Service: North America Tel Fax info.america@elekta.com Europe, Middle East, Africa, Eastern Europe, Latin America Tel Fax info.europe@elekta.com Asia Pacific Tel Fax info.asia@elekta.com Human Care Makes the Future Possible Art. nr MKT [02] 2015 Elekta AB (publ). All mentioned trademarks and registered trademarks are the property of the Elekta Group. All rights reserved. No part of this document may be reproduced in any form without written permission from the copyright holder. The names of other companies and products mentioned herein are used for identification purposes only and may be trademarks or registered trademarks of their respective owners.