- Email: [email protected]
Monte Carlo simulations to optimize experimental dosimetry of narrow beams used in Gamma Knife radio-surgery
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 580 (2007) 548–551 www.elsevier.com/locate/nima
Monte Carlo simulations to optimize experimental dosimetry of narrow beams used in Gamma Knife radio-surgery G. Lymperopouloua,, L. Petrokokkinosa, P. Papagiannisa, M. Steinerb, V. Spevacekb, J. Semnickab, P. Dvorakb, I. Seimenisa a Nuclear and Particle Physics Section, Physics Department, University of Athens, Panepistimioupolis, Ilisia, 157 71 Athens, Greece Czech Technical University, Faculty of Nuclear Sciences and Physical Engineering, Department of Dosimetry and Application of Ionizing Radiation, Brehova 7 115 19, Praha 1, Czech Republic
b
Available online 24 May 2007
Abstract The Leksell Gamma Knife is a stereotactic radio-surgery unit for the treatment of small volumes (on the order of 25 mm3) that employs a hemispherical configuration of 201 60Co sources and appropriate configurations of collimation to form beams of 4, 8, 14 and 18 mm nominal diameter at the Unit Center Point (UCP). Although Monte Carlo (MC) simulation is well suited for narrow-beam dosimetry, experimental dosimetry is required at least for acceptance testing and quality assurance purposes. Besides other drawbacks of conventional point dosimeters, the main problems associated with narrow-beam dosimetry in stereotactic applications are accurate positioning and volume averaging. In this work, MCNPX and EGSnrc MC simulation dosimetry results for a Gamma Knife unit are benchmarked through their comparison to treatment planning software calculations based on radio-chromic film measurements. Then, MC dosimetry results are utilized to optimize the only three-dimensional experimental dosimetry method available; the polymer gelMagnetic Resonance Imaging (MRI) method. MC results are used to select the spatial resolution in the imaging session of the irradiated gels and validate a mathematical tool for the localization of the UCP in the three-dimensional experimental dosimetry data acquired. Experimental results are compared with corresponding MC calculations and shown capable to provide accurate dosimetry, free of volume averaging and positioning uncertainties. r 2007 Elsevier B.V. All rights reserved. PACS: 87.53.Ly; 87.53.Bn; 87.53.Dq Keywords: Dosimetry; Radio-surgery; Polymer gels; MRI
1. Introduction Various narrow beam, stereotactic, radiation therapy techniques are used in an effort to increase dose conformity to the target thus sparing healthy nearby structures. The Leksell Gamma Knife unit [1,2] employs a hemispherical configuration of 201 60Co sources, a stable primary collimator system and four final collimator helmets to form beams of 4, 8, 14 and 18 mm nominal diameter at the Unit Center Point (UCP), the mechanical center of the machine. Single or multiple shots of these beams are Corresponding author. Tel.: +30 210 727 6944; fax: +30 210 727 6987.
E-mail address: [email protected] (G. Lymperopoulou). 0168-9002/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2007.05.227
programmed and delivered to patients using a stereotactic frame fixated to their head to achieve sub-mm accuracy. While Monte Carlo (MC) simulation obviates the problems associated with the dosimetry of narrow beams through its versatility in geometric modeling, scoring geometry and tally methods, experimental dosimetry is required at least for acceptance testing and quality assurance purposes. Besides, however the problems associated with the use of conventional dosimeters (dose rate or directional dependence, poor reproducibility, lack of lateral electronic equilibrium, etc.) [3] even contemporary three-dimensional (3D) methods such as the polymer gelMagnetic Resonance Imaging (MRI) could suffer by volume averaging and positioning uncertainties.
ARTICLE IN PRESS G. Lymperopoulou et al. / Nuclear Instruments and Methods in Physics Research A 580 (2007) 548–551
In this work, MC simulation dosimetry is performed using two different codes and photon field sampling techniques. Results are benchmarked and used to optimize polymer gel-MRI as an efficient, stand-alone dosimetry tool in single Gamma Knife collimator helmet shots. 2. Materials and methods 2.1. Monte Carlo simulations Both the EGSnrc [4] and MCNPX [5] codes were used for simulations in this work. In EGSnrc simulations, the exact geometry and materials of a single beam channel were modeled including the bushing assembly with cobalt source, the stationary collimator and the final collimators. To increase efficiency, the location and direction vectors of photons exiting this channel were transformed using appropriate rotation matrices to simulate the radiation field modulated by the hemispherical configuration of the 201 channels. In MCNPX simulations, the simplified geometry proposed by Al-Dweri and Lallena [6] was used where each source channel is simulated by a point source emitting the initial photons in the cone defined by itself and the helmet outer collimators of given apertures and maximum polar angle for each helmet. A water phantom of 16 cm diameter was used in simulations with both codes, centered at the UCP. Appropriate energy deposition scoring procedures were used with each code employing full tracking of secondary electrons. Simulations were performed for all collimator helmets using various voxel sizes. A number of initial photon histories on the order of 108 were used that resulted in statistical uncertainty of 1% at scoring voxels close to the UCP and about 3% at distant points within each collimator helmet shot. 2.2. Polymer gel-MRI dosimetry An experimental methodology for polymer gel Gamma Knife dosimetry has been described [7,8] that uses multimodality fiducial markers to define a reference coordinate system throughout the setup, treatment planning, irradiation, MRI readout and image processing. This methodology was also used in this work to irradiate PABIG gel [8] filled vials inside a 16-cm-diameter PMMA spherical phantom with 30 Gy at the UCP for each of the four collimator helmets. Another vial was irradiated with 30 Gy at one 4 mm and one 8 mm shot using the default Output Factor (OF) values, and a sixth vial was irradiated with a single brachytherapy source dwell position to provide an R2-dose calibration curve [7,8]. All vials were scanned 7 days postirradiation on a 1.5 T whole-body Philips ACS NT MR imager using a 3D dual echo TSE sequence (Turbo Factor ¼ 64, TE1 ¼ 40 ms, TE2 ¼ 800 ms, TR ¼ 2300 ms, acquisition time of 5 min 36 s). The T2 (spin–spin relaxation time) 3D matrices were automatically produced by the imager software and then
549
converted to relaxation rate (R2 ¼ 1/T2) matrices and, finally, normalized percentage dose matrices. In each T2 matrix of single-shot irradiated gels, the UCP was geometrically determined by the markers. Additionally, a mathematical tool for finding the ‘center of mass’ of a 3D object was benchmarked using MC results and employed with 3D polymer gel results to localize the UCP in each shot. In brief, a 3D object was created in each T2 matrix by setting measurement voxel T2 values equal to unity or zero depending on whether they were lower or greater, respectively, than a set T2 threshold value. The ‘center of mass’ and the axis of symmetry of the 3D object were then calculated. Due to the symmetry of the dose distribution, these results correspond to a number of independent estimates of the UCP with an uncertainty equal to the standard deviation of the mean. 3. Results and discussion Fig. 1 presents the comparison of EGSnrc and MCNPX results of two different scoring resolutions with corresponding Leksell GammaPlan calculations. MC data sets by both codes are in close agreement to GammaPlan results verifying that the amount of scattered photons by the collimators contributes negligible effects to beam dose profiles [2,9]. Moreover, the agreement of MC results with 0.5 and 1 mm scoring resolution suggests that spatial resolution in that range is suitable for Gamma Knife dosimetry. This is an important information for polymer gel dosimetry where improving the spatial resolution in the MRI session significantly prolongs the scanning time. Irradiated gels in this work were therefore scanned using a voxel dimension of 0.75 0.75 0.75 mm3. MC dose distributions were used to benchmark the UCP localization tool that was found to achieve sub-imaging voxel accuracy relative to the marker method that has an uncertainty of at least half the MRI voxel size. For example, the UCP in the 4 mm shot irradiated gel was found to reside at (x, y, z) ¼ (100.3470.12, 99.9070.04, 100.1570.22) relative to the position planned using the multimodality markers of (100, 100, 100). Fig. 2 presents indicative results of the comparison between MC calculations and polymer gel-MRI measurements. A close agreement may be observed except for very low dose points where experimental results fluctuate due to the methods’ dose resolution combined with the relatively poor SNR of the imaging session which is another trade off in imaging time. Besides dose profiles, the GammaPlan treatment planning software requires the input of OFs for each collimator helmet relative to the largest (18 mm). The OF values, especially for the smaller helmets, have received focus in the literature [2]. With the aid of the developed UCP localization tool, an OF measurement methodology that obviates potential gel intra-batch variability and other relevant sources of error is the irradiation of a single gel vial with two helmet shots as
ARTICLE IN PRESS 550
G. Lymperopoulou et al. / Nuclear Instruments and Methods in Physics Research A 580 (2007) 548–551
Fig. 1. EGSnrc (* and + correspond to 1 mm and 0.5 scoring resolution), MCNPX (J) and Leksell GammaPlan (full line) results of percentage, relative dose profiles along the x and z axes of the Gamma Knife unit for the smallest (4 mm upper panel) and largest (18 mm lower panel) collimator helmets.
Fig. 2. EGSnrc calculated (J) and polymer gel-MRI measured (*) results of percentage, relative dose profiles along the x and z axes of the Gamma Knife unit for the smallest collimator helmet (4 mm).
depicted in Fig. 3. The UCPs in each shot in this vial were found to differ by (Dx, Dy, Dz) ¼ (0.11, 0.03, 19.52) mm relative to (0, 0, 20) mm according to dose delivery planning.
Fig. 4 shows the profile of raw measured R2 values along the line passing through the UCP at each shot. Since the two shots of equal dose were delivered using the default OFs, the agreement of measured signal is a crude
ARTICLE IN PRESS G. Lymperopoulou et al. / Nuclear Instruments and Methods in Physics Research A 580 (2007) 548–551
verification of these conclusions cannot mechanical integrity the imaging session. the experiment.
551
OF values. However, more accurate be drawn due to potential loss of of the gelatin matrix or poor SNR of Further work is in progress to repeat
4. Conclusions Monte Carlo dosimetry can be performed using simplified geometry modeling Gamma Knife stereotactic radiosurgery dosimetry. It was also used to optimize the polymer gel-MRI dosimetry method. This method could be further standardized to evolve in a stand-alone tool for all the prerequisite dosimetric parameters for Gamma Knife treatment planning. Acknowledgments This study was supported by a Greece–Czech joint research and technology program (2005–2007). References
Fig. 3. The central T2 image of the vial irradiated with one 4 mm and one 8 mm shot.
Fig. 4. The R2 profile along the direction marked in Fig. 3.
[1] L. Leksell, Acta Chir. Scand. 102 (1951) 316. [2] A. Mack, S.G. Scheib, J. Major, S. Gianolini, G. Pazmandi, H. Feist, H. Czempiel, H.J. Kreiner, Med. Phys. 29 (2002) 2080. [3] M. Heydarian, P.W. Hoban, A.H. Beddoe, Phys. Med. Biol. 41 (1996) 93. [4] I. Kawrakow, D.W.O. Rogers, NRCC Report PIRS-701, 2001. [5] L. S. Waters (Ed.), MCNPX User’s Manual Version 2.4.0, Los Alamos National Laboratory Report LA-CP-02-408, 2002. [6] F.M.O. Al Dweri, A.M. Lallena, Phys. Med. Biol. 49 (2004) 3441. [7] P. Karaiskos, L. Petrokokkinos, E. Tatsis, A. Angelopoulos, P. Baras, M. Kozicki, P. Papagiannis, J.M. Rosiak, L. Sakelliou, P. Sandilos, L. Vlachos, Phys. Med. Biol. 50 (2005) 1235. [8] P. Papagiannis, P. Karaiskos, M. Kozicki, J.M. Rosiak, L. Sakelliou, P. Sandilos, I. Seimenis, M. Torrens, Phys. Med. Biol. 50 (2005) 1979. [9] J.Y.C. Cheung, K.N. Yu, Med. Phys. 33 (2006) 41.
Nuclear Instruments and Methods in Physics Research A 580 (2007) 548–551 www.elsevier.com/locate/nima
Monte Carlo simulations to optimize experimental dosimetry of narrow beams used in Gamma Knife radio-surgery G. Lymperopouloua,, L. Petrokokkinosa, P. Papagiannisa, M. Steinerb, V. Spevacekb, J. Semnickab, P. Dvorakb, I. Seimenisa a Nuclear and Particle Physics Section, Physics Department, University of Athens, Panepistimioupolis, Ilisia, 157 71 Athens, Greece Czech Technical University, Faculty of Nuclear Sciences and Physical Engineering, Department of Dosimetry and Application of Ionizing Radiation, Brehova 7 115 19, Praha 1, Czech Republic
b
Available online 24 May 2007
Abstract The Leksell Gamma Knife is a stereotactic radio-surgery unit for the treatment of small volumes (on the order of 25 mm3) that employs a hemispherical configuration of 201 60Co sources and appropriate configurations of collimation to form beams of 4, 8, 14 and 18 mm nominal diameter at the Unit Center Point (UCP). Although Monte Carlo (MC) simulation is well suited for narrow-beam dosimetry, experimental dosimetry is required at least for acceptance testing and quality assurance purposes. Besides other drawbacks of conventional point dosimeters, the main problems associated with narrow-beam dosimetry in stereotactic applications are accurate positioning and volume averaging. In this work, MCNPX and EGSnrc MC simulation dosimetry results for a Gamma Knife unit are benchmarked through their comparison to treatment planning software calculations based on radio-chromic film measurements. Then, MC dosimetry results are utilized to optimize the only three-dimensional experimental dosimetry method available; the polymer gelMagnetic Resonance Imaging (MRI) method. MC results are used to select the spatial resolution in the imaging session of the irradiated gels and validate a mathematical tool for the localization of the UCP in the three-dimensional experimental dosimetry data acquired. Experimental results are compared with corresponding MC calculations and shown capable to provide accurate dosimetry, free of volume averaging and positioning uncertainties. r 2007 Elsevier B.V. All rights reserved. PACS: 87.53.Ly; 87.53.Bn; 87.53.Dq Keywords: Dosimetry; Radio-surgery; Polymer gels; MRI
1. Introduction Various narrow beam, stereotactic, radiation therapy techniques are used in an effort to increase dose conformity to the target thus sparing healthy nearby structures. The Leksell Gamma Knife unit [1,2] employs a hemispherical configuration of 201 60Co sources, a stable primary collimator system and four final collimator helmets to form beams of 4, 8, 14 and 18 mm nominal diameter at the Unit Center Point (UCP), the mechanical center of the machine. Single or multiple shots of these beams are Corresponding author. Tel.: +30 210 727 6944; fax: +30 210 727 6987.
E-mail address: [email protected] (G. Lymperopoulou). 0168-9002/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2007.05.227
programmed and delivered to patients using a stereotactic frame fixated to their head to achieve sub-mm accuracy. While Monte Carlo (MC) simulation obviates the problems associated with the dosimetry of narrow beams through its versatility in geometric modeling, scoring geometry and tally methods, experimental dosimetry is required at least for acceptance testing and quality assurance purposes. Besides, however the problems associated with the use of conventional dosimeters (dose rate or directional dependence, poor reproducibility, lack of lateral electronic equilibrium, etc.) [3] even contemporary three-dimensional (3D) methods such as the polymer gelMagnetic Resonance Imaging (MRI) could suffer by volume averaging and positioning uncertainties.
ARTICLE IN PRESS G. Lymperopoulou et al. / Nuclear Instruments and Methods in Physics Research A 580 (2007) 548–551
In this work, MC simulation dosimetry is performed using two different codes and photon field sampling techniques. Results are benchmarked and used to optimize polymer gel-MRI as an efficient, stand-alone dosimetry tool in single Gamma Knife collimator helmet shots. 2. Materials and methods 2.1. Monte Carlo simulations Both the EGSnrc [4] and MCNPX [5] codes were used for simulations in this work. In EGSnrc simulations, the exact geometry and materials of a single beam channel were modeled including the bushing assembly with cobalt source, the stationary collimator and the final collimators. To increase efficiency, the location and direction vectors of photons exiting this channel were transformed using appropriate rotation matrices to simulate the radiation field modulated by the hemispherical configuration of the 201 channels. In MCNPX simulations, the simplified geometry proposed by Al-Dweri and Lallena [6] was used where each source channel is simulated by a point source emitting the initial photons in the cone defined by itself and the helmet outer collimators of given apertures and maximum polar angle for each helmet. A water phantom of 16 cm diameter was used in simulations with both codes, centered at the UCP. Appropriate energy deposition scoring procedures were used with each code employing full tracking of secondary electrons. Simulations were performed for all collimator helmets using various voxel sizes. A number of initial photon histories on the order of 108 were used that resulted in statistical uncertainty of 1% at scoring voxels close to the UCP and about 3% at distant points within each collimator helmet shot. 2.2. Polymer gel-MRI dosimetry An experimental methodology for polymer gel Gamma Knife dosimetry has been described [7,8] that uses multimodality fiducial markers to define a reference coordinate system throughout the setup, treatment planning, irradiation, MRI readout and image processing. This methodology was also used in this work to irradiate PABIG gel [8] filled vials inside a 16-cm-diameter PMMA spherical phantom with 30 Gy at the UCP for each of the four collimator helmets. Another vial was irradiated with 30 Gy at one 4 mm and one 8 mm shot using the default Output Factor (OF) values, and a sixth vial was irradiated with a single brachytherapy source dwell position to provide an R2-dose calibration curve [7,8]. All vials were scanned 7 days postirradiation on a 1.5 T whole-body Philips ACS NT MR imager using a 3D dual echo TSE sequence (Turbo Factor ¼ 64, TE1 ¼ 40 ms, TE2 ¼ 800 ms, TR ¼ 2300 ms, acquisition time of 5 min 36 s). The T2 (spin–spin relaxation time) 3D matrices were automatically produced by the imager software and then
549
converted to relaxation rate (R2 ¼ 1/T2) matrices and, finally, normalized percentage dose matrices. In each T2 matrix of single-shot irradiated gels, the UCP was geometrically determined by the markers. Additionally, a mathematical tool for finding the ‘center of mass’ of a 3D object was benchmarked using MC results and employed with 3D polymer gel results to localize the UCP in each shot. In brief, a 3D object was created in each T2 matrix by setting measurement voxel T2 values equal to unity or zero depending on whether they were lower or greater, respectively, than a set T2 threshold value. The ‘center of mass’ and the axis of symmetry of the 3D object were then calculated. Due to the symmetry of the dose distribution, these results correspond to a number of independent estimates of the UCP with an uncertainty equal to the standard deviation of the mean. 3. Results and discussion Fig. 1 presents the comparison of EGSnrc and MCNPX results of two different scoring resolutions with corresponding Leksell GammaPlan calculations. MC data sets by both codes are in close agreement to GammaPlan results verifying that the amount of scattered photons by the collimators contributes negligible effects to beam dose profiles [2,9]. Moreover, the agreement of MC results with 0.5 and 1 mm scoring resolution suggests that spatial resolution in that range is suitable for Gamma Knife dosimetry. This is an important information for polymer gel dosimetry where improving the spatial resolution in the MRI session significantly prolongs the scanning time. Irradiated gels in this work were therefore scanned using a voxel dimension of 0.75 0.75 0.75 mm3. MC dose distributions were used to benchmark the UCP localization tool that was found to achieve sub-imaging voxel accuracy relative to the marker method that has an uncertainty of at least half the MRI voxel size. For example, the UCP in the 4 mm shot irradiated gel was found to reside at (x, y, z) ¼ (100.3470.12, 99.9070.04, 100.1570.22) relative to the position planned using the multimodality markers of (100, 100, 100). Fig. 2 presents indicative results of the comparison between MC calculations and polymer gel-MRI measurements. A close agreement may be observed except for very low dose points where experimental results fluctuate due to the methods’ dose resolution combined with the relatively poor SNR of the imaging session which is another trade off in imaging time. Besides dose profiles, the GammaPlan treatment planning software requires the input of OFs for each collimator helmet relative to the largest (18 mm). The OF values, especially for the smaller helmets, have received focus in the literature [2]. With the aid of the developed UCP localization tool, an OF measurement methodology that obviates potential gel intra-batch variability and other relevant sources of error is the irradiation of a single gel vial with two helmet shots as
ARTICLE IN PRESS 550
G. Lymperopoulou et al. / Nuclear Instruments and Methods in Physics Research A 580 (2007) 548–551
Fig. 1. EGSnrc (* and + correspond to 1 mm and 0.5 scoring resolution), MCNPX (J) and Leksell GammaPlan (full line) results of percentage, relative dose profiles along the x and z axes of the Gamma Knife unit for the smallest (4 mm upper panel) and largest (18 mm lower panel) collimator helmets.
Fig. 2. EGSnrc calculated (J) and polymer gel-MRI measured (*) results of percentage, relative dose profiles along the x and z axes of the Gamma Knife unit for the smallest collimator helmet (4 mm).
depicted in Fig. 3. The UCPs in each shot in this vial were found to differ by (Dx, Dy, Dz) ¼ (0.11, 0.03, 19.52) mm relative to (0, 0, 20) mm according to dose delivery planning.
Fig. 4 shows the profile of raw measured R2 values along the line passing through the UCP at each shot. Since the two shots of equal dose were delivered using the default OFs, the agreement of measured signal is a crude
ARTICLE IN PRESS G. Lymperopoulou et al. / Nuclear Instruments and Methods in Physics Research A 580 (2007) 548–551
verification of these conclusions cannot mechanical integrity the imaging session. the experiment.
551
OF values. However, more accurate be drawn due to potential loss of of the gelatin matrix or poor SNR of Further work is in progress to repeat
4. Conclusions Monte Carlo dosimetry can be performed using simplified geometry modeling Gamma Knife stereotactic radiosurgery dosimetry. It was also used to optimize the polymer gel-MRI dosimetry method. This method could be further standardized to evolve in a stand-alone tool for all the prerequisite dosimetric parameters for Gamma Knife treatment planning. Acknowledgments This study was supported by a Greece–Czech joint research and technology program (2005–2007). References
Fig. 3. The central T2 image of the vial irradiated with one 4 mm and one 8 mm shot.
Fig. 4. The R2 profile along the direction marked in Fig. 3.
[1] L. Leksell, Acta Chir. Scand. 102 (1951) 316. [2] A. Mack, S.G. Scheib, J. Major, S. Gianolini, G. Pazmandi, H. Feist, H. Czempiel, H.J. Kreiner, Med. Phys. 29 (2002) 2080. [3] M. Heydarian, P.W. Hoban, A.H. Beddoe, Phys. Med. Biol. 41 (1996) 93. [4] I. Kawrakow, D.W.O. Rogers, NRCC Report PIRS-701, 2001. [5] L. S. Waters (Ed.), MCNPX User’s Manual Version 2.4.0, Los Alamos National Laboratory Report LA-CP-02-408, 2002. [6] F.M.O. Al Dweri, A.M. Lallena, Phys. Med. Biol. 49 (2004) 3441. [7] P. Karaiskos, L. Petrokokkinos, E. Tatsis, A. Angelopoulos, P. Baras, M. Kozicki, P. Papagiannis, J.M. Rosiak, L. Sakelliou, P. Sandilos, L. Vlachos, Phys. Med. Biol. 50 (2005) 1235. [8] P. Papagiannis, P. Karaiskos, M. Kozicki, J.M. Rosiak, L. Sakelliou, P. Sandilos, I. Seimenis, M. Torrens, Phys. Med. Biol. 50 (2005) 1979. [9] J.Y.C. Cheung, K.N. Yu, Med. Phys. 33 (2006) 41.