Radiol Phys Technol DOI 10.1007/s12194-014-0266-1
Three-dimensional gamma analysis of dose distributions in individual structures for IMRT dose verification Yuuki Tomiyama • Fujio Araki • Takeshi Oono • Kazunari Hioki
Received: 1 November 2013 / Revised: 2 April 2014 / Accepted: 3 April 2014 Ó Japanese Society of Radiological Technology and Japan Society of Medical Physics 2014
Abstract Our purpose in this study was to implement three-dimensional (3D) gamma analysis for structures of interest such as the planning target volume (PTV) or clinical target volume (CTV), and organs at risk (OARs) for intensity-modulated radiation therapy (IMRT) dose verification. IMRT dose distributions for prostate and head and neck (HN) cancer patients were calculated with an analytical anisotropic algorithm in an Eclipse (Varian Medical Systems) treatment planning system (TPS) and by Monte Carlo (MC) simulation. The MC dose distributions were calculated with EGSnrc/BEAMnrc and DOSXYZnrc user codes under conditions identical to those for the TPS. The prescribed doses were 76 Gy/38 fractions with fivefield IMRT for the prostate and 33 Gy/17 fractions with seven-field IMRT for the HN. TPS dose distributions were verified by the gamma passing rates for the whole calculated volume, PTV or CTV, and OARs by use of 3D gamma analysis with reference to MC dose distributions. The acceptance criteria for the 3D gamma analysis were 3/3 and 2 %/2 mm for a dose difference and a distance to agreement. The gamma passing rates in PTV and OARs for the prostate IMRT plan were close to 100 %. For the HN IMRT plan, the passing rates of 2 %/2 mm in CTV and OARs were substantially lower because inhomogeneous tissues such as bone and air in the HN are included in the calculation area. 3D gamma analysis for individual structures is useful for IMRT dose verification. Keywords Gamma index Structure IMRT Monte Carlo calculation MATLAB software Y. Tomiyama (&) F. Araki T. Oono K. Hioki Graduate School of Health Sciences, Kumamoto University, 4-24-1 Kuhonji, Kumamoto, Japan e-mail: [email protected]
1 Introduction With the clinical utilization of advanced radiotherapy techniques such as intensity-modulated radiation therapy (IMRT), the dose distributions have been more complex and diverse, and patient-specific dose verification has been needed prior to a treatment procedure. Many dose verification studies have been performed for evaluation of the accuracy of dose calculations in the treatment planning system (TPS). The dose evaluations have been carried out by comparison of TPS-calculated dose distributions with those measured by two-dimensional (2D) and threedimensional (3D) dosimeters, or calculated by high-precision algorithms such as the Monte Carlo (MC) method [1, 2]. The MC method can accurately simulate the random walk of an individual particle in materials by means of radiation transport calculation. In addition, the head configuration of a linear accelerator that includes a multileaf collimator is able to be modeled in detail with generalpurpose MC codes [3, 4]. The MC method is useful for estimation of dose distributions in heterogeneous regions in patients for the radiation therapy where dose measurements are not easy. The methods for quantitatively comparing dose distributions obtained with different types of instruments have been developed by many authors [5–8]. Gamma analysis is one of the major methods for quantitative comparison of dose distributions and was introduced by Low et al. [5]. The gamma method has been evaluated and modified by several authors [9–15]. In this method, the gamma index is calculated from acceptance criteria of a dose difference (DD) and a distance to agreement (DTA), which represents the consistency of two dose distributions, termed the reference and the evaluated dose distributions. Either one or both distributions may be measured or calculated. The
Y. Tomiyama et al.
gamma index is calculated independently for each reference point by use of the entire evaluated distribution. The quantitative analysis is performed by means of the gamma passing rate, which shows the percentage of ‘‘gamma index B1’’ in a region of interest. The passing rate is generally calculated for the whole measured or calculated area, or for the area defined by application of a userspecified threshold level to reference dose distributions. However, calculating gamma indexes for the numbers of reference points takes much time. It is also difficult to identify the anatomic locations in which dose discrepancies between reference and evaluated dose distributions are produced. Furthermore, the passing rates for the whole dose distribution and anatomic structures do not always correlate. Therefore, besides the 3D gamma analysis for the whole calculated volume, that for structures of interest such as the planning target volume (PTV) or clinical target volume (CTV) and organs at risk (OARs) are required for quantitative evaluation between the reference and evaluated dose distributions. Several studies [16–19] have been carried out on the evaluation of dose distributions in individual structures by 3D gamma analysis. These studies implemented the dose verification using 3D dose distributions modified from planned patient distributions. Any differences between the measured and planned planar dose distributions in a homogeneous phantom are added in the 3D dose distributions. The measurements were performed with a homogeneous phantom by conventional per-beam planar dose quality assurance methods. The modification of planned patient dose distributions was done by an algorithm called ‘‘planned dose perturbation’’ (PDP) and implemented with 3DVH software (Sun Nuclear Corporation), translating the differences between the measured and planned planar dose distributions in the phantom. The performance of the 3DVH software and the PDP algorithm is described in previous studies [16–19]. However, the verification method in previous studies did not consider inhomogeneities in the patient body. Therefore, the 3D gamma analysis for IMRT dose verification could be useful to be performed for individual structures using dose distributions estimated in patient geometry (CT images). In this study, we implemented the 3D gamma analysis of dose distributions in individual structures for IMRT dose verification using the MC-calculated dose distribution as reference. The 3D gamma analysis was performed with inhouse software created by MATLAB (R2007b, MathWorks). IMRT dose distributions for prostate and head and neck (HN) cancer patients were calculated with the TPS and the MC methods. TPS dose distributions were verified by the passing rates for the whole calculated volume, PTV or CTV, and OARs for MC dose distributions by use of 3D gamma analysis with the reference to MC dose distributions.
Bone
Soft tissue
Lung
Air
Fig. 1 Conversion curve of CT number to materials and mass density
2 Methods and materials 2.1 Treatment planning Intensity-modulated radiation therapy treatment planning for prostate and HN cancer patients was performed with an Eclipse (ver.10.0.28, Varian Medical Systems) TPS. The prescribed doses were 76 Gy/38 fractions with five-field IMRT for the prostate case and 33 Gy/17 fractions with seven-field IMRT for the HN case. Dose distributions for each IMRT plan were calculated with an analytical anisotropic algorithm (AAA) in Eclipse. The calculation area included the patient immobilization device for the prostate case and both of the patient immobilization device and the treatment couch for the HN case. The calculation grid sizes were 2.5 9 2.5 9 2.5 mm3 and 3 9 3 9 2.5 mm3 for the prostate and HN plans, respectively. The treatment machine was a Clinac iX (Varian Medical Systems) equipped with a Millennium 120 multileaf collimator. 2.2 Monte Carlo simulation For MC dose calculation, a voxel-based phantom (MC phantom) was created by conversion of planning CT images (CT number) into materials (air, lung, soft tissue, and bone) and mass densities. The conversion curve of the CT number to materials and mass density is shown in Fig. 1. The voxel-based phantom was developed by use of the function based on the DICOM-RT toolbox [20]. The phantom grid size was matched to that of the TPS. MC dose distributions for each treatment field were calculated under conditions identical to the TPS by means of the EGSnrc/BEAMnrc [21] and DOSXYZnrc [22] user codes. The photon and electron cut-off energies were 0.01 and 0.7 MeV, respectively. Next, the MC dose distributions were calibrated with the absorbed dose-to-water per
Three-dimensional gamma analysis of dose distributions
Fig. 2 Dose distributions at an axial slice, calculated with a AAA and b MC, and c DVHs in each structure for a prostate IMRT plan
monitor unit and multiplied by the same monitor units to the TPS for each treatment field. Finally, all treatment IMRT fields were summed and outputted as ‘‘3ddose file’’. 2.3 Three-dimensional gamma analysis The gamma evaluation combines a DD criterion and a DTA criterion for comparison of two dose distributions: an evaluated dose distribution, De ! re , and a reference dose ! distribution, Dr rr . The labels are necessary because the result of the gamma evaluation is not symmetric with respect to which distribution is selected for each role [10]. ! The DD, d ! re ; rr , is defined as ! ! r D ! r ; ð1Þ d r ;r ¼D ! e
r
e
e
r
r
! and the spatial distance, r ! re ; rr , is defined as ! ! ! ! r re ; rr ¼ re rr : The generalized C function is defined as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! !ffi ! ! d2 ! re ; rr r2 ! re ; rr ; þ C re ; rr ¼ DD2 Dd 2
ð2Þ
ð3Þ
where DD and Dd are the acceptance criteria for DD and DTA, respectively. As acceptance criterion DD for the DD, a local criterion can be used, e.g., 3 % of the local dose, or
a global criterion, e.g., 3 % of the prescribed dose. The gamma index is defined as ! ! c ! rr ¼ min C ! re ; rr 8 re : ð4Þ ! ! The gamma index is the minimum C re ; rr that the evaluated point is the best match to the reference point. If c ! rr 1, the evaluated distribution is accepted at that point, and the percentage of the accepted points in any structure is evaluated as the gamma passing rate. For performing the quantitative 3D gamma analysis, dose distributions and structure sets generated in the TPS were imported to the MATLAB software in DICOM-RT format. The MC-calculated 3ddose files were also imported to the software. In this study, dose distributions of TPS and MC were assigned as reference and evaluated dose distributions, respectively. The 3D gamma index distributions for IMRT dose distributions for the prostate and HN were calculated based on the work of Wendling et al. [14]. The evaluated dose distributions were linearly interpolated and had a voxel spacing of 0.5 9 0.5 9 0.5 mm3. The maximum search distance was 5 mm from each reference point, and DD and Dd were 3/3 and 2 %/2 mm in each 3D gamma distribution. The DDs were reported as a percentage of the prescribed dose for each IMRT plan [23]. The gamma passing rates in each structure for acceptance criteria and dose volume histograms (DVHs) were also evaluated for both IMRT plans for the
Y. Tomiyama et al.
Fig. 3 3D gamma index distributions with 3 %/3 mm criteria for a prostate IMRT plan. a Coronal, b sagittal, and c axial views Table 1 3D gamma passing rates in each structure for a prostate IMRT plan
Structures
Criteria 3 %/ 3 mm (%)
Body
2 %/ 2 mm (%)
90.2
85.8
Bladder
100.0
100.0
Rectum PTV
100.0 99.9
100.0 99.1
Lt. pelvis
100.0
98.1
Rt. pelvis
100.0
98.4
prostate and HN by use of the 3D gamma index distributions. The 3D gamma analysis was performed with an in-house program developed by use of the MATLAB software. 3 Results and discussion 3.1 Prostate IMRT plan The prostate IMRT dose distributions and DVHs calculated with AAA and MC are shown in Fig. 2a to c respectively.
Similarly, the 3D gamma distributions with 3 %/3 mm criteria are shown in Fig. 3a to c. These distributions show the magnitude of the difference between two dose distributions for given DD/DTA criteria. From the DVHs, the two dose distributions were in good agreement with 0.1, 0.7, and 0.6 % for mean doses to the PTV, bladder, and rectum, respectively. Table 1 shows the 3D gamma passing rates in each structure for a prostate IMRT plan. The passing rate for ‘‘body’’ structure was calculated by inclusion of the whole dose distribution volume. The passing rates in the body were 90.2 and 85.8 % for 3/3 and 2 %/2 mm criteria, respectively. The passing rates decreased due to DDs in the air region between the patient body and the immobilization device, as seen in Fig. 3. This is because the dose kernel in AAA is modeled assuming that the elemental composition is the same as that of water, and consequently it does not take into account the elemental composition of air. In contrast, the passing rates in PTV and OAR structures were close to 100 % for both criteria. The results show the importance of dose evaluation in every structure based on the 3D gamma analysis. This method makes it possible to evaluate dose distributions quantitatively in every structure, unlike the conventional gamma method based on whole dose distributions.
Three-dimensional gamma analysis of dose distributions
Fig. 4 Dose distributions at an axial slice calculated with a AAA and b MC, and c DVHs in each structure for a head and neck plan
Table 2 3D gamma passing rates in each structure for a head and neck IMRT plan
Structures
Criteria 3 %/ 3 mm (%)
Body Brain stem
2 %/2 mm (%)
79.6
69.1
100.0
98.2
Spinal cord
99.3
85.6
CTV
91.3
75.6
Lt. parotid
98.7
88.8
Rt. parotid
100.0
100.0
3.2 Head and neck IMRT plan The HN IMRT dose distributions and DVHs calculated with the AAA and MC are shown in Fig. 4a to c respectively. Similarly, Fig 5a to c show the 3D gamma distributions with 3 %/3 mm criteria. From the DVHs, the differences between two dose distributions were 6.2 % for D95 of CTV and 2.5, 3.9, 1.5, and 1.3 % for mean doses to the right parotid, left parotid, brainstem, and spinal cord, respectively. Table 2 shows the 3D gamma passing rates in each structure for an HN IMRT plan. The passing rates for the body were 79.6 and 69.1 % for 3/3 and 2 %/2 mm criteria, respectively. These decreases in the passing rates for the body occurred because of the DD in the treatment couch, as
seen in Fig. 5. Because the AAA cannot accurately model the lateral electron transport, DDs with MC are observed in low density regions such as the treatment couch. Additionally, the results show lower passing rates than the prostate IMRT plan. This is because the HN includes complexly inhomogeneous tissues such as bone and air, unlike the prostate. Consequently, the inhomogeneous tissues decrease the dose calculation accuracy of AAA. The passing rate in CTV decreased from 91.3 % for 3 %/ 3 mm criteria to 75.6 % for 2 %/2 mm criteria. Because the dose kernel in the AAA is modeled assuming the elemental composition of water as mentioned before, DDs with the MC calculation occur in regions for bone or air inside or around the CTV. Consequently, the AAA overestimates the absorbed dose in the CTV compared with MC. The passing rates in the OARs also show a tendency similar to that for the CTV for 2 %/2 mm criteria. The 3D gamma analysis of individual structures for an HN IMRT plan is useful for the dose evaluation of the PTV and OARs compared to the conventional gamma method because the head and neck have complex anatomic structures, unlike the prostate. Although Fig. 4c shows the DDs between the AAA and MC in DVHs, the passing rate in any structure for 3 %/ 3 mm criteria was above 90 %, as shown in Table 2. In particular, the gamma passing rates in the right parotid were 100 % for criteria of both 3/3 and 2 %/2 mm, in spite
Y. Tomiyama et al.
Fig. 5 3D gamma index distributions with 3 %/3 mm criteria for a head and neck plan. a Coronal, b sagittal, and c axial views
of the existence of a 2.5 % mean DD on the DVH. This implies that the gamma passing rate does not always reflect the DDs on DVHs. Several investigators [16–19] have studied the relationship between gamma passing rates and DDs on DVHs. They have reported that there are only weak correlations between gamma passing rates and DVH values for target and OAR volumes. The gamma passing rates do not include information on the magnitude of dose errors. Therefore, one should use not only the gamma passing rates, but also the gamma distributions, gamma histograms, and DVHs for the quantitative evaluation of dose distributions. Moreover, using the specific criteria for the target or OARs helps the quantitative evaluation. Further investigations about the selection of suitable parameters are strongly recommended for 3D gamma analysis.
4 Conclusion In this study, we implemented a 3D gamma analysis of individual structures for IMRT dose verification by
comparing TPS and MC-calculated dose distributions. The 3D gamma analysis for IMRT dose distributions inside structures was useful for quantitative evaluation of dose calculation accuracy in TPS. Conflict of interest of interest.
The authors declare that they have no conflict
References 1. Sterpin E, Tomsej M, Smedt BD, Reynaert N, et al. Monte Carlo evaluation of the AAA treatment planning algorithm in a heterogeneous multilayer phantom and IMRT clinical treatments for an Elekta SL25 linear accelerator. Med Phys. 2007;34:1665–77. 2. Goetzfriend T, Rickhey M, Treuwein M, Koelbl O, et al. Monte Carlo simulations to replace film dosimetry in IMRT verification. Z Med Phys. 2011;21:19–25. 3. Rogers DWO, Faddegon BA, Ding GX, Ma CM, et al. BEAM: a Monte Carlo code to simulate radiotherapy treatment units. Med Phys. 1995;22:503–24. 4. Kim JO, Siebers JV, Keall PJ, Arnfield MR, et al. A Monte Carlo study of radiation transport through multileaf collimators. Med Phys. 2001;28:2497–506.
Three-dimensional gamma analysis of dose distributions 5. Low DA, Harms WB, Mutic S, Purdy JA. A technique for the quantitative evaluation of dose distributions. Med Phys. 1998;25:656–72. 6. Childress NL, Rosen II. The design and testing of novel clinical parameters for dose comparison. Int J Radiat Oncol Biol Phys. 2003;56:1464–79. 7. Blanpain B, Mercier D. The delta envelope: a technique for dose distribution comparison. Med Phys. 2009;36:797–808. 8. Moran JM, Radawski J, Fraass BA. A dose gradient analysis tool for IMRT QA. J Appl Clin Med Phys. 2005;6:62–73. 9. Depuydt T, Van Esch A, Huyskens DP. A quantitative evaluation of IMRT dose distributions: refinement and clinical assessment of the gamma evaluation. Radiother Oncol. 2002;62: 309–19. 10. Low DA, Dempsey JF. Evaluation of the gamma dose distribution comparison method. Med Phys. 2003;30:2455–64. 11. Stock M, Kroupa B, Georg D. Interpretation and evaluation of the gamma index and the gamma index angle for the verification of IMRT hybrid plans. Phys Med Biol. 2005;50: 399–411. 12. Bakai A, Alber M, Nusslin F. A revision of the gamma-evaluation concept for the comparison of dose distributions. Phys Med Biol. 2003;48:3543–53. 13. Spezi E, Lewis DG. Gamma histograms for radiotherapy plan evaluation. Radiother Oncol. 2006;79:224–30. 14. Wendling M, Zijp LJ, McDermott LN, Smit EJ, et al. A fast algorithm for gamma evaluation in 3D. Med Phys. 2007;34: 1647–54.
15. Ju T, Simpson T, Deasy JO, Low DA. Geometric interpretation of the gamma dose distribution comparison technique: interpolationfree calculation. Med Phys. 2008;35:879–87. 16. Zhen H, Nelms BE, Tome´ WA. Moving from gamma passing rates to patient DVH-based QA metrics in pretreatment dose QA. Med Phys. 2011;38:5477–89. 17. Nelms BE, Zhen H, Tome´ WA. Per-beam, planar IMRT QA passing rates do not predict clinically relevant patient dose errors. Med Phys. 2011;38:1037–44. 18. Carrasco P, Jornet N, Latorre A, Eudaldo T, et al. 3D DVH-based metric analysis versus per-beam planar analysis in IMRT pretreatment verification. Med Phys. 2012;39:5040–9. 19. Stasi M, Bresciani S, Miranti A, Maggio A, et al. Pretreatment patient-specific IMRT quality assurance: a correlation study between gamma index and patient clinical dose volume histogram. Med Phys. 2012;39:7626–34. 20. Spezi E, Lewis DG, Smith CW. A DICOM-RT-based toolbox for the evaluation and verification of radiotherapy plans. Phys Med Biol. 2002;47:4223–32. 21. Rogers DWO, Walters B, Kawrakow I. BEAMnrc users manual. National Research Council of Canada, Ottawa, NRCC Report PIRS-0509(A). 2011. 22. Walters B, Kawrakow I, Rogers DWO. DOSXYZnrc users manual. National Research Council of Canada, Ottawa, NRCC Report PIRS-794revB. 2011. 23. Van Dyk J, Barnett RB, Cygler JE, Shragge PC. Commissioning and quality assurance of treatment planning computers. Int J Radiat Oncol Biol Phys. 1993;26:261–73.
Three-dimensional gamma analysis of dose distributions in individual structures for IMRT dose verification Yuuki Tomiyama • Fujio Araki • Takeshi Oono • Kazunari Hioki
Received: 1 November 2013 / Revised: 2 April 2014 / Accepted: 3 April 2014 Ó Japanese Society of Radiological Technology and Japan Society of Medical Physics 2014
Abstract Our purpose in this study was to implement three-dimensional (3D) gamma analysis for structures of interest such as the planning target volume (PTV) or clinical target volume (CTV), and organs at risk (OARs) for intensity-modulated radiation therapy (IMRT) dose verification. IMRT dose distributions for prostate and head and neck (HN) cancer patients were calculated with an analytical anisotropic algorithm in an Eclipse (Varian Medical Systems) treatment planning system (TPS) and by Monte Carlo (MC) simulation. The MC dose distributions were calculated with EGSnrc/BEAMnrc and DOSXYZnrc user codes under conditions identical to those for the TPS. The prescribed doses were 76 Gy/38 fractions with fivefield IMRT for the prostate and 33 Gy/17 fractions with seven-field IMRT for the HN. TPS dose distributions were verified by the gamma passing rates for the whole calculated volume, PTV or CTV, and OARs by use of 3D gamma analysis with reference to MC dose distributions. The acceptance criteria for the 3D gamma analysis were 3/3 and 2 %/2 mm for a dose difference and a distance to agreement. The gamma passing rates in PTV and OARs for the prostate IMRT plan were close to 100 %. For the HN IMRT plan, the passing rates of 2 %/2 mm in CTV and OARs were substantially lower because inhomogeneous tissues such as bone and air in the HN are included in the calculation area. 3D gamma analysis for individual structures is useful for IMRT dose verification. Keywords Gamma index Structure IMRT Monte Carlo calculation MATLAB software Y. Tomiyama (&) F. Araki T. Oono K. Hioki Graduate School of Health Sciences, Kumamoto University, 4-24-1 Kuhonji, Kumamoto, Japan e-mail: [email protected]
1 Introduction With the clinical utilization of advanced radiotherapy techniques such as intensity-modulated radiation therapy (IMRT), the dose distributions have been more complex and diverse, and patient-specific dose verification has been needed prior to a treatment procedure. Many dose verification studies have been performed for evaluation of the accuracy of dose calculations in the treatment planning system (TPS). The dose evaluations have been carried out by comparison of TPS-calculated dose distributions with those measured by two-dimensional (2D) and threedimensional (3D) dosimeters, or calculated by high-precision algorithms such as the Monte Carlo (MC) method [1, 2]. The MC method can accurately simulate the random walk of an individual particle in materials by means of radiation transport calculation. In addition, the head configuration of a linear accelerator that includes a multileaf collimator is able to be modeled in detail with generalpurpose MC codes [3, 4]. The MC method is useful for estimation of dose distributions in heterogeneous regions in patients for the radiation therapy where dose measurements are not easy. The methods for quantitatively comparing dose distributions obtained with different types of instruments have been developed by many authors [5–8]. Gamma analysis is one of the major methods for quantitative comparison of dose distributions and was introduced by Low et al. [5]. The gamma method has been evaluated and modified by several authors [9–15]. In this method, the gamma index is calculated from acceptance criteria of a dose difference (DD) and a distance to agreement (DTA), which represents the consistency of two dose distributions, termed the reference and the evaluated dose distributions. Either one or both distributions may be measured or calculated. The
Y. Tomiyama et al.
gamma index is calculated independently for each reference point by use of the entire evaluated distribution. The quantitative analysis is performed by means of the gamma passing rate, which shows the percentage of ‘‘gamma index B1’’ in a region of interest. The passing rate is generally calculated for the whole measured or calculated area, or for the area defined by application of a userspecified threshold level to reference dose distributions. However, calculating gamma indexes for the numbers of reference points takes much time. It is also difficult to identify the anatomic locations in which dose discrepancies between reference and evaluated dose distributions are produced. Furthermore, the passing rates for the whole dose distribution and anatomic structures do not always correlate. Therefore, besides the 3D gamma analysis for the whole calculated volume, that for structures of interest such as the planning target volume (PTV) or clinical target volume (CTV) and organs at risk (OARs) are required for quantitative evaluation between the reference and evaluated dose distributions. Several studies [16–19] have been carried out on the evaluation of dose distributions in individual structures by 3D gamma analysis. These studies implemented the dose verification using 3D dose distributions modified from planned patient distributions. Any differences between the measured and planned planar dose distributions in a homogeneous phantom are added in the 3D dose distributions. The measurements were performed with a homogeneous phantom by conventional per-beam planar dose quality assurance methods. The modification of planned patient dose distributions was done by an algorithm called ‘‘planned dose perturbation’’ (PDP) and implemented with 3DVH software (Sun Nuclear Corporation), translating the differences between the measured and planned planar dose distributions in the phantom. The performance of the 3DVH software and the PDP algorithm is described in previous studies [16–19]. However, the verification method in previous studies did not consider inhomogeneities in the patient body. Therefore, the 3D gamma analysis for IMRT dose verification could be useful to be performed for individual structures using dose distributions estimated in patient geometry (CT images). In this study, we implemented the 3D gamma analysis of dose distributions in individual structures for IMRT dose verification using the MC-calculated dose distribution as reference. The 3D gamma analysis was performed with inhouse software created by MATLAB (R2007b, MathWorks). IMRT dose distributions for prostate and head and neck (HN) cancer patients were calculated with the TPS and the MC methods. TPS dose distributions were verified by the passing rates for the whole calculated volume, PTV or CTV, and OARs for MC dose distributions by use of 3D gamma analysis with the reference to MC dose distributions.
Bone
Soft tissue
Lung
Air
Fig. 1 Conversion curve of CT number to materials and mass density
2 Methods and materials 2.1 Treatment planning Intensity-modulated radiation therapy treatment planning for prostate and HN cancer patients was performed with an Eclipse (ver.10.0.28, Varian Medical Systems) TPS. The prescribed doses were 76 Gy/38 fractions with five-field IMRT for the prostate case and 33 Gy/17 fractions with seven-field IMRT for the HN case. Dose distributions for each IMRT plan were calculated with an analytical anisotropic algorithm (AAA) in Eclipse. The calculation area included the patient immobilization device for the prostate case and both of the patient immobilization device and the treatment couch for the HN case. The calculation grid sizes were 2.5 9 2.5 9 2.5 mm3 and 3 9 3 9 2.5 mm3 for the prostate and HN plans, respectively. The treatment machine was a Clinac iX (Varian Medical Systems) equipped with a Millennium 120 multileaf collimator. 2.2 Monte Carlo simulation For MC dose calculation, a voxel-based phantom (MC phantom) was created by conversion of planning CT images (CT number) into materials (air, lung, soft tissue, and bone) and mass densities. The conversion curve of the CT number to materials and mass density is shown in Fig. 1. The voxel-based phantom was developed by use of the function based on the DICOM-RT toolbox [20]. The phantom grid size was matched to that of the TPS. MC dose distributions for each treatment field were calculated under conditions identical to the TPS by means of the EGSnrc/BEAMnrc [21] and DOSXYZnrc [22] user codes. The photon and electron cut-off energies were 0.01 and 0.7 MeV, respectively. Next, the MC dose distributions were calibrated with the absorbed dose-to-water per
Three-dimensional gamma analysis of dose distributions
Fig. 2 Dose distributions at an axial slice, calculated with a AAA and b MC, and c DVHs in each structure for a prostate IMRT plan
monitor unit and multiplied by the same monitor units to the TPS for each treatment field. Finally, all treatment IMRT fields were summed and outputted as ‘‘3ddose file’’. 2.3 Three-dimensional gamma analysis The gamma evaluation combines a DD criterion and a DTA criterion for comparison of two dose distributions: an evaluated dose distribution, De ! re , and a reference dose ! distribution, Dr rr . The labels are necessary because the result of the gamma evaluation is not symmetric with respect to which distribution is selected for each role [10]. ! The DD, d ! re ; rr , is defined as ! ! r D ! r ; ð1Þ d r ;r ¼D ! e
r
e
e
r
r
! and the spatial distance, r ! re ; rr , is defined as ! ! ! ! r re ; rr ¼ re rr : The generalized C function is defined as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! !ffi ! ! d2 ! re ; rr r2 ! re ; rr ; þ C re ; rr ¼ DD2 Dd 2
ð2Þ
ð3Þ
where DD and Dd are the acceptance criteria for DD and DTA, respectively. As acceptance criterion DD for the DD, a local criterion can be used, e.g., 3 % of the local dose, or
a global criterion, e.g., 3 % of the prescribed dose. The gamma index is defined as ! ! c ! rr ¼ min C ! re ; rr 8 re : ð4Þ ! ! The gamma index is the minimum C re ; rr that the evaluated point is the best match to the reference point. If c ! rr 1, the evaluated distribution is accepted at that point, and the percentage of the accepted points in any structure is evaluated as the gamma passing rate. For performing the quantitative 3D gamma analysis, dose distributions and structure sets generated in the TPS were imported to the MATLAB software in DICOM-RT format. The MC-calculated 3ddose files were also imported to the software. In this study, dose distributions of TPS and MC were assigned as reference and evaluated dose distributions, respectively. The 3D gamma index distributions for IMRT dose distributions for the prostate and HN were calculated based on the work of Wendling et al. [14]. The evaluated dose distributions were linearly interpolated and had a voxel spacing of 0.5 9 0.5 9 0.5 mm3. The maximum search distance was 5 mm from each reference point, and DD and Dd were 3/3 and 2 %/2 mm in each 3D gamma distribution. The DDs were reported as a percentage of the prescribed dose for each IMRT plan [23]. The gamma passing rates in each structure for acceptance criteria and dose volume histograms (DVHs) were also evaluated for both IMRT plans for the
Y. Tomiyama et al.
Fig. 3 3D gamma index distributions with 3 %/3 mm criteria for a prostate IMRT plan. a Coronal, b sagittal, and c axial views Table 1 3D gamma passing rates in each structure for a prostate IMRT plan
Structures
Criteria 3 %/ 3 mm (%)
Body
2 %/ 2 mm (%)
90.2
85.8
Bladder
100.0
100.0
Rectum PTV
100.0 99.9
100.0 99.1
Lt. pelvis
100.0
98.1
Rt. pelvis
100.0
98.4
prostate and HN by use of the 3D gamma index distributions. The 3D gamma analysis was performed with an in-house program developed by use of the MATLAB software. 3 Results and discussion 3.1 Prostate IMRT plan The prostate IMRT dose distributions and DVHs calculated with AAA and MC are shown in Fig. 2a to c respectively.
Similarly, the 3D gamma distributions with 3 %/3 mm criteria are shown in Fig. 3a to c. These distributions show the magnitude of the difference between two dose distributions for given DD/DTA criteria. From the DVHs, the two dose distributions were in good agreement with 0.1, 0.7, and 0.6 % for mean doses to the PTV, bladder, and rectum, respectively. Table 1 shows the 3D gamma passing rates in each structure for a prostate IMRT plan. The passing rate for ‘‘body’’ structure was calculated by inclusion of the whole dose distribution volume. The passing rates in the body were 90.2 and 85.8 % for 3/3 and 2 %/2 mm criteria, respectively. The passing rates decreased due to DDs in the air region between the patient body and the immobilization device, as seen in Fig. 3. This is because the dose kernel in AAA is modeled assuming that the elemental composition is the same as that of water, and consequently it does not take into account the elemental composition of air. In contrast, the passing rates in PTV and OAR structures were close to 100 % for both criteria. The results show the importance of dose evaluation in every structure based on the 3D gamma analysis. This method makes it possible to evaluate dose distributions quantitatively in every structure, unlike the conventional gamma method based on whole dose distributions.
Three-dimensional gamma analysis of dose distributions
Fig. 4 Dose distributions at an axial slice calculated with a AAA and b MC, and c DVHs in each structure for a head and neck plan
Table 2 3D gamma passing rates in each structure for a head and neck IMRT plan
Structures
Criteria 3 %/ 3 mm (%)
Body Brain stem
2 %/2 mm (%)
79.6
69.1
100.0
98.2
Spinal cord
99.3
85.6
CTV
91.3
75.6
Lt. parotid
98.7
88.8
Rt. parotid
100.0
100.0
3.2 Head and neck IMRT plan The HN IMRT dose distributions and DVHs calculated with the AAA and MC are shown in Fig. 4a to c respectively. Similarly, Fig 5a to c show the 3D gamma distributions with 3 %/3 mm criteria. From the DVHs, the differences between two dose distributions were 6.2 % for D95 of CTV and 2.5, 3.9, 1.5, and 1.3 % for mean doses to the right parotid, left parotid, brainstem, and spinal cord, respectively. Table 2 shows the 3D gamma passing rates in each structure for an HN IMRT plan. The passing rates for the body were 79.6 and 69.1 % for 3/3 and 2 %/2 mm criteria, respectively. These decreases in the passing rates for the body occurred because of the DD in the treatment couch, as
seen in Fig. 5. Because the AAA cannot accurately model the lateral electron transport, DDs with MC are observed in low density regions such as the treatment couch. Additionally, the results show lower passing rates than the prostate IMRT plan. This is because the HN includes complexly inhomogeneous tissues such as bone and air, unlike the prostate. Consequently, the inhomogeneous tissues decrease the dose calculation accuracy of AAA. The passing rate in CTV decreased from 91.3 % for 3 %/ 3 mm criteria to 75.6 % for 2 %/2 mm criteria. Because the dose kernel in the AAA is modeled assuming the elemental composition of water as mentioned before, DDs with the MC calculation occur in regions for bone or air inside or around the CTV. Consequently, the AAA overestimates the absorbed dose in the CTV compared with MC. The passing rates in the OARs also show a tendency similar to that for the CTV for 2 %/2 mm criteria. The 3D gamma analysis of individual structures for an HN IMRT plan is useful for the dose evaluation of the PTV and OARs compared to the conventional gamma method because the head and neck have complex anatomic structures, unlike the prostate. Although Fig. 4c shows the DDs between the AAA and MC in DVHs, the passing rate in any structure for 3 %/ 3 mm criteria was above 90 %, as shown in Table 2. In particular, the gamma passing rates in the right parotid were 100 % for criteria of both 3/3 and 2 %/2 mm, in spite
Y. Tomiyama et al.
Fig. 5 3D gamma index distributions with 3 %/3 mm criteria for a head and neck plan. a Coronal, b sagittal, and c axial views
of the existence of a 2.5 % mean DD on the DVH. This implies that the gamma passing rate does not always reflect the DDs on DVHs. Several investigators [16–19] have studied the relationship between gamma passing rates and DDs on DVHs. They have reported that there are only weak correlations between gamma passing rates and DVH values for target and OAR volumes. The gamma passing rates do not include information on the magnitude of dose errors. Therefore, one should use not only the gamma passing rates, but also the gamma distributions, gamma histograms, and DVHs for the quantitative evaluation of dose distributions. Moreover, using the specific criteria for the target or OARs helps the quantitative evaluation. Further investigations about the selection of suitable parameters are strongly recommended for 3D gamma analysis.
4 Conclusion In this study, we implemented a 3D gamma analysis of individual structures for IMRT dose verification by
comparing TPS and MC-calculated dose distributions. The 3D gamma analysis for IMRT dose distributions inside structures was useful for quantitative evaluation of dose calculation accuracy in TPS. Conflict of interest of interest.
The authors declare that they have no conflict
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