Verification and Dosimetric Impact of Acuros XB Algorithm for Stereotactic Body Radiation Therapy (SBRT) and RapidArc Planning for Non-Small-Cell Lung Cancer (NSCLC) Patients

Affiliation(s)

Department of Medical Physics, ProCure Proton Therapy Center, Oklahoma City, USA.

Department of Radiation Oncology, Arizona Center for Cancer Care, Peoria, USA.

Department of Medical Physics, ProCure Proton Therapy Center, Oklahoma City, USA.

Department of Radiation Oncology, Arizona Center for Cancer Care, Peoria, USA.

ABSTRACT

**Purpose:** The experimental verification of the Acuros XB (AXB) algorithm was conducted in
a heterogeneous rectangular slab phantom, and compared to the Anisotropic
Analytical Algorithm (AAA). The dosimetric impact of the AXB for stereotactic
body radiation therapy (SBRT) and RapidArc planning for 16 non-small-cell lung
cancer (NSCLC) patients
was assessed due to the dose recalculation from the AAA to the AXB. **Methods:** The calculated central axis percentage depth doses
(PDD) in a heterogeneous slab phantom for an open field size of 3 ×3 cm^{2} were
compared against the PDD measured by an
ionization chamber. For 16 NSCLC patients, the dose-volume parameters from the
treatment plans calculated by the AXB and the AAA were compared using identical
jaw settings, leaf positions, and monitor units (MUs). **Results:** The results from the heterogeneous slab phantom study
showed that the AXB was more accurate than the AAA; however, the dose
underestimation by the AXB (up to ?3.9%) and AAA (up to ?13.5%) was observed.
For a planning target volume (PTV) in the NSCLC patients, in comparison to the
AAA, the AXB predicted lower mean and minimum doses by average 0.3% and 4.3%
respectively, but a higher maximum dose by average 2.3%. The averaged maximum
doses to the heart and spinal cord predicted by the AXB were lower by 1.3% and
2.6% respectively; whereas the doses to the lungs predicted by the AXB were
higher by up to 0.5% compared to the AAA. The percentage of ipsilateral lung volume
receiving at least 20 and 5 Gy (V20 and V5 respectively) were higher in the AXB
plans than in the AAA plans by average 1.1% and 2.8% respectively. The AXB
plans produced higher target heterogeneity by average 4.5% and lower plan
conformity by average 5.8% compared to the AAA plans. Using the AXB, the PTV
coverage (95% of the PTV covered by the 100% of the prescribed dose) was
reduced by average 8.2% than using the AAA. The AXB plans required about 2.3%
increment in the number of MUs in order to achieve the same PTV coverage as in
the AAA plans. **Conclusion: **The AXB
is more accurate to use for the dose calculations in SBRT lung plans created
with a RapidArc technique; however, one should also note the reduced PTV
coverage due to the dose recalculation from the AAA to the AXB.

Cite this paper

S. Rana, K. Rogers, T. Lee, D. Reed and C. Biggs, "Verification and Dosimetric Impact of Acuros XB Algorithm for Stereotactic Body Radiation Therapy (SBRT) and RapidArc Planning for Non-Small-Cell Lung Cancer (NSCLC) Patients,"*International Journal of Medical Physics, Clinical Engineering and Radiation Oncology*, Vol. 2 No. 1, 2013, pp. 6-14. doi: 10.4236/ijmpcero.2013.21002.

S. Rana, K. Rogers, T. Lee, D. Reed and C. Biggs, "Verification and Dosimetric Impact of Acuros XB Algorithm for Stereotactic Body Radiation Therapy (SBRT) and RapidArc Planning for Non-Small-Cell Lung Cancer (NSCLC) Patients,"

References

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[6] J. Chow, M. Seguin and A. Alexander, “Dosimetric Effect of Collimating Jaws for Small Multileaf Collimated Fields,” Medical Physics, Vol. 32, No. 3, 2005, pp. 759765. doi:10.1118/1.1861413

[7] T. Kn??s, E. Wieslander, L. Cozzi, C. Brink, A. Fogliata, D. Albers, H. Nystr?m and S. Lassen, “Comparison of Dose Calculation Algorithms for Treatment Planning in External Photon Beam Therapy for Clinical Situations,” Physics in Medicine and Biology, Vol. 51, No. 22, 2006, pp. 5785-807. doi:10.1088/0031-9155/51/22/005

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[9] B. Dobler, C. Walter, A. Knopf, D. Fabri, R. Loeschel, M. Polednik, F. Schneider and F. Lohr, “Optimization of Extracranial Stereotactic Radiation Therapy of Small Lung Lesions Using Accurate Dose Calculation Algorithms,” Radiation Oncology, Vol. 1, No. 45, 2006. doi:10.1186/1748-717X-1-45

[10] B. Vanderstraeten, N. Reynaert, L. Paelinck , I. Madani, C. De Wagter, W. De Gersem, W. De Neve and H. Thierens, “Accuracy of Patient Dose Calculation for Lung IMRT: A Comparison of Monte Carlo, Convolution/Superposition, and Pencil Beam Computations,” Medical Physics, Vol. 33, No. 9, pp. 3149-3158. doi:10.1118/1.2241992

[11] T. Krieger and O. Sauer, “Monte Carloversus PencilBeam-/Collapsed-Cone-Dose Calculation in a Heterogeneous Multi-Layer Phantom,” Physics in Medicine and Biology, Vol. 50, No. 5, 2005, pp. 859-868. doi:10.1088/0031-9155/50/5/010

[12] A. Gray, L. Oliver and P. Johnson, “The Accuracy of the Pencil Beam Convolution and Anisotropic Analytical Algorithms in Predicting the Dose Effects Due to the Attenuation from Immobilization Devices and Large Air Gaps,” Medical Physics, Vol. 36, No. 7, 2009, pp. 31813191. doi:10.1118/1.3147204

[13] D. Robinson, “Inhomogeneity Correction and the Analytic Anisotropic Algorithm,” Journal of Applied Clinical Medical Physics, Vol. 9, No. 2, 2008, pp. 112-122.

[14] A. Van Esch, L. Tillikainen, J. Pyykkonen, M. Tenhunen, H. Helminen, Siljam?ki S, J. Alakuijala, M. Paiusco, M. Lori and D. Huyskens, “Testing of the Analytical Anisotropic Algorithm for Photon Dose Calculation,” Medical Physics, Vol. 33, No. 11, 2006, pp. 4130-4148. doi:10.1118/1.2358333

[15] S. Rana and and K. Rogers, “Dosimetric Evaluation with Acuros XB dose Calculation Algorithm with Measurements in Predicting Doses beyond Different Air Gap Thickness for Smaller and Larger Field Sizes,” Journal of Medical Physics, Vol. 38, No. 1, 2013, pp. 9-14. doi:10.4103/0971-6203.106600

[16] R. Ottosson, A. Karlsson and C. Behrens, “Pareto Front Analysis of 6 and 15 MV Dynamic IMRT for Lung Cancer Using Pencil Beam, AAA and Monte Carlo,” Physics in Medicine and Biology, Vol. 55, No. 16, 2010, pp. 4521-4533. doi:10.1088/0031-9155/55/16/S07

[17] P. Carrasco, N. Jornet, M. Duch, L. Weber, M. Ginjaume, T. Eudaldo, D. Jurado, A. Ruiz and M. Ribas, “Comparison of Dose Calculation Algorithms in Phantoms with Lung Equivalent Heterogeneities Under Conditions of Lateral Electronic Disequilibrium,” Medical Physics, Vol. 31, No. 10, 2004, pp. 2899-2911. doi:10.1118/1.1788932

[18] N. Reynaert, S. van der Marck, D. Schaart, W. Van der Zee, C. Van Vliet-Vroegindeweij, M. Tomsej, J. Jansen, B. Heijmen, M. Coghe and C. De Wagter, “Monte Carlo Treatment Planning for Photon and Electron Beams,” Radiation Physics and Chemistry, Vol. 76, No. 4, 2007, pp. 643-686. doi:10.1016/j.radphyschem.2006.05.015

[19] O. Vassiliev, T. Wareing T, J. McGhee, G. Failla, M. Salehpour and F. Mourtada, “Validation of a New Grid Based Blotzmann Equation Solver for Dose Calculation In Radiotherapy With Photon Beams,” Physics in Medicine and Biology, Vol. 55, No. 3, 2010, pp. 581-598. doi:10.1088/0031-9155/55/3/002

[20] T. Han, J. Mikell, M. Salehpour and Mourtada F, “Dosimetric Comparison of Acuros XB Deterministic Radiation Transport Method with Monte Carlo and ModelBased Convolution Methods in Heterogeneous Media,” Medical Physics, Vol. 38, No. 5, 2011, pp. 2651-2664. doi:10.1118/1.3582690

[21] K. Bush, I. Gagne, S. Zavgorodni, W. Ansbacher and W. Beckham, “Dosimetric Validation of Acuros XB with Monte Carlo Methods for Photon Dose Calculations,” Medical Physics, Vol. 38, No. 4, 2011, pp. 2208-2221. doi:10.1118/1.3567146

[22] A. Fogliata, G. Nicolini, A. Clivio, E. Vanetti and L. Cozzi, “Dosimetric Evaluation of Acuros XB Advanced Dose Calculation algorithm in heterogeneous media,” Radiation Oncology, Vol. 6, No. 82, 2011. doi:10.1186/1748-717X-6-82

[23] M. Kan, L. Leung and P. Yu, “Verification and Dosimetric Impact of Acuros XB Algorithm on Intensity Modulated Stereotactic Radiotherapy for Locally Persistent Nasopharyngeal Carcinoma,” Medical Physics, Vol. 39, No. 8, 2012, pp. 4705-4714. doi:10.1118/1.4736819

[24] T. Han, F. Mourtada, K. Kisling, J. Mikell, D. Followill and R. Howell, “Experimental Validation of Deterministic Acuros XB algorithm for IMRT and VMAT Dose Calculations with the Radiological Physics Center’s Head and Neck Phantom,” Medical Physics, Vol. 39, No. 4, 2012, Article ID: 2193. doi:10.1118/1.3692180

[25] L. Hoffmann, M. J?rgensen, L. Muren and J. Petersen, “Clinical Validation of the Acuros XB Photon Dose Calculation Algorithm, a Grid-Based Boltzmann Equation Solver,” Acta Oncologica, Vol. 51, No. 3, 2012, pp. 376385. doi:10.3109/0284186X.2011.629209

[26] A. Fogliata, G. Nicolini, A. Clivio, E. Vanetti and L. Cozzi, “On the Dosimetric Impact of Inhomogeneity Management In the Acuros XB Algorithm for Breast Treatment,” Radiation Oncology, Vol. 6, No. 103, 2011. doi:10.1186/1748-717X-6-103

[27] A. Fogliata, G. Nicolini, A. Clivio, E. Vanetti and L. Cozzi, “Critical Appraisal of Acuros XB and Anisotropic Analytic Algorithm Dose Calculation in Advanced NonSmall-Cell Lung Cancer Treatments,” International Journal of Radiation Oncology, Biology and Physics, Vol. 183, No. 5, 2012, pp. 1587-1595. doi:10.1016/j.ijrobp.2011.10.078

[28] L. Tillikainen, H. Helminen, T. Torsti, S. Siljam?ki, J. Alakuijala, J. Pyyry J and W. Ulmer, “3D Pencil-BeamBased Superposition Algorithm for Photon Dose Calculation in Heterogeneous Media,” Physics in Medicine and Biology, Vol. 53, No. 14, 2008, pp. 3821-3839. doi:10.1088/0031-9155/53/14/008

[29] I. Paddick I, “A simple Scoring Ratio to Index the Conformity of Radiosurgical Treatment Plans,” Technical Note, Journal of Neurosurgery, Vol. 93, No. 3, 2000, pp. 219-222.

[30] N. Papanikolaou, J. Battista, A. Boyer, C. Kappas, C. Klein, T. Mackie, M. Sharpe and J. Van Dyke, “Tissue Inhomogeneity Corrections for Megavoltage Photon Beams,” The American Association of Physicist in Medicine, College Park, 2004.

[31] C. Martens, N. Reynaert, C. De Wagter, P. Nilsson, M. Coghe, H. Palmans, H. Thierens and W. De Neve, “Underdosage of the Upper-Airway Mucosa for Small Fields as Used in Intensity-Modulated Radiation Therapy: A Comparison Between Radiochromic Film Measurements, Monte Carlo Simulations, and Collapsed Cone Convolution Calculations,” Medical Physics, Vol. 29, No. 7, 2002, pp. 1528-1535. doi:10.1118/1.1487421

[32] B. Vanderstraeten, N. Reynaert, L. Paelinck, I. Madani, C. De Wagter, W. De Gersem, W. De Neve and H. Thierens, “Accuracy of Patient Dose Calculation for Lung IMRT: A Comparison of Monte Carlo, Convolution/Superposition, and Pencil Beam Computations,” Medical Physics, Vol. 33, No. 9, 2006, pp. 3149-3158. doi:10.1118/1.2241992

[33] W. De Neve and C. De Wagter, “Lethal Pneumonitis in a Phase I Study of Chemotherapy and IMRT for NSCLC: the Need to Investigate the Accuracy of Dose Computation,” Radiotherapy Oncology, Vol. 75, No. 2, 2005, pp. 246-247. doi:10.1016/j.radonc.2005.03.024

[34] R. Kornelsen and M.Young, “Changes in the Dose-Profile of a 10 MV X-Ray Beam Within and Beyond Low Density Material,” Medical Physics, Vol. 9, No. 1, 1982, pp. 114-116. doi:10.1118/1.595059

[1] American Cancer Society, “Cancer Facts and Figures,” 2012. http://www.cancer.org

[2] A. Fakiris A, R. McGarry R, C. Yiannoutsos C, L. Papiez, M. Williams, M. Henderson and R. Timmerman , “Stereotactic Body Radiation Therapy for Early Stage Nonsmall Cell Lung Carcinoma: Four-Year Results of a Prospective Phase II Study,” International Journal of Radiation Oncology, Biology and Physics, Vol. 75, No. 3, 2009, pp. 677-682. doi:10.1016/j.ijrobp.2008.11.042

[3] F. Zimmermann, H. Geinitz, S. Schill, A. Grosu, U. Schratzenstaller, M. Molls and B. Jeremic, “Stereotactic Hypofractionated Radiation Therapy for Stage I Non-Small Cell Lung Cancer,” Lung Cancer, Vol. 48, No. 1, 2005, pp. 107-114. doi:10.1016/j.lungcan.2004.10.015

[4] D. Schuring and C. Hurkmans, “Developing and Evaluating Stereotactic Lung RT Trials: What We Should Know about the Influence of Inhomogeneity Corrections on Dose,” Radiation Oncology, Vol. 3, No. 21, 2008. doi:10.1186/1748-717X-3-21

[5] I. Das, G. Ding and A. Ahnesjo, “Small Fields: Nonequilibrium Radiation Dosimetry,” Medical Physics, Vol. 35, No. 1, 2008, pp. 206-215. doi:10.1118/1.2815356

[6] J. Chow, M. Seguin and A. Alexander, “Dosimetric Effect of Collimating Jaws for Small Multileaf Collimated Fields,” Medical Physics, Vol. 32, No. 3, 2005, pp. 759765. doi:10.1118/1.1861413

[7] T. Kn??s, E. Wieslander, L. Cozzi, C. Brink, A. Fogliata, D. Albers, H. Nystr?m and S. Lassen, “Comparison of Dose Calculation Algorithms for Treatment Planning in External Photon Beam Therapy for Clinical Situations,” Physics in Medicine and Biology, Vol. 51, No. 22, 2006, pp. 5785-807. doi:10.1088/0031-9155/51/22/005

[8] J. Dutreix, A. Dutreix and M. Tubiana, “Electronic Equilibrium and Transition Stages,” Physics in Medicine and Biology, Vol. 10, No. 2, 1965, pp. 177-190. doi:10.1088/0031-9155/10/2/302

[9] B. Dobler, C. Walter, A. Knopf, D. Fabri, R. Loeschel, M. Polednik, F. Schneider and F. Lohr, “Optimization of Extracranial Stereotactic Radiation Therapy of Small Lung Lesions Using Accurate Dose Calculation Algorithms,” Radiation Oncology, Vol. 1, No. 45, 2006. doi:10.1186/1748-717X-1-45

[10] B. Vanderstraeten, N. Reynaert, L. Paelinck , I. Madani, C. De Wagter, W. De Gersem, W. De Neve and H. Thierens, “Accuracy of Patient Dose Calculation for Lung IMRT: A Comparison of Monte Carlo, Convolution/Superposition, and Pencil Beam Computations,” Medical Physics, Vol. 33, No. 9, pp. 3149-3158. doi:10.1118/1.2241992

[11] T. Krieger and O. Sauer, “Monte Carloversus PencilBeam-/Collapsed-Cone-Dose Calculation in a Heterogeneous Multi-Layer Phantom,” Physics in Medicine and Biology, Vol. 50, No. 5, 2005, pp. 859-868. doi:10.1088/0031-9155/50/5/010

[12] A. Gray, L. Oliver and P. Johnson, “The Accuracy of the Pencil Beam Convolution and Anisotropic Analytical Algorithms in Predicting the Dose Effects Due to the Attenuation from Immobilization Devices and Large Air Gaps,” Medical Physics, Vol. 36, No. 7, 2009, pp. 31813191. doi:10.1118/1.3147204

[13] D. Robinson, “Inhomogeneity Correction and the Analytic Anisotropic Algorithm,” Journal of Applied Clinical Medical Physics, Vol. 9, No. 2, 2008, pp. 112-122.

[14] A. Van Esch, L. Tillikainen, J. Pyykkonen, M. Tenhunen, H. Helminen, Siljam?ki S, J. Alakuijala, M. Paiusco, M. Lori and D. Huyskens, “Testing of the Analytical Anisotropic Algorithm for Photon Dose Calculation,” Medical Physics, Vol. 33, No. 11, 2006, pp. 4130-4148. doi:10.1118/1.2358333

[15] S. Rana and and K. Rogers, “Dosimetric Evaluation with Acuros XB dose Calculation Algorithm with Measurements in Predicting Doses beyond Different Air Gap Thickness for Smaller and Larger Field Sizes,” Journal of Medical Physics, Vol. 38, No. 1, 2013, pp. 9-14. doi:10.4103/0971-6203.106600

[16] R. Ottosson, A. Karlsson and C. Behrens, “Pareto Front Analysis of 6 and 15 MV Dynamic IMRT for Lung Cancer Using Pencil Beam, AAA and Monte Carlo,” Physics in Medicine and Biology, Vol. 55, No. 16, 2010, pp. 4521-4533. doi:10.1088/0031-9155/55/16/S07

[17] P. Carrasco, N. Jornet, M. Duch, L. Weber, M. Ginjaume, T. Eudaldo, D. Jurado, A. Ruiz and M. Ribas, “Comparison of Dose Calculation Algorithms in Phantoms with Lung Equivalent Heterogeneities Under Conditions of Lateral Electronic Disequilibrium,” Medical Physics, Vol. 31, No. 10, 2004, pp. 2899-2911. doi:10.1118/1.1788932

[18] N. Reynaert, S. van der Marck, D. Schaart, W. Van der Zee, C. Van Vliet-Vroegindeweij, M. Tomsej, J. Jansen, B. Heijmen, M. Coghe and C. De Wagter, “Monte Carlo Treatment Planning for Photon and Electron Beams,” Radiation Physics and Chemistry, Vol. 76, No. 4, 2007, pp. 643-686. doi:10.1016/j.radphyschem.2006.05.015

[19] O. Vassiliev, T. Wareing T, J. McGhee, G. Failla, M. Salehpour and F. Mourtada, “Validation of a New Grid Based Blotzmann Equation Solver for Dose Calculation In Radiotherapy With Photon Beams,” Physics in Medicine and Biology, Vol. 55, No. 3, 2010, pp. 581-598. doi:10.1088/0031-9155/55/3/002

[20] T. Han, J. Mikell, M. Salehpour and Mourtada F, “Dosimetric Comparison of Acuros XB Deterministic Radiation Transport Method with Monte Carlo and ModelBased Convolution Methods in Heterogeneous Media,” Medical Physics, Vol. 38, No. 5, 2011, pp. 2651-2664. doi:10.1118/1.3582690

[21] K. Bush, I. Gagne, S. Zavgorodni, W. Ansbacher and W. Beckham, “Dosimetric Validation of Acuros XB with Monte Carlo Methods for Photon Dose Calculations,” Medical Physics, Vol. 38, No. 4, 2011, pp. 2208-2221. doi:10.1118/1.3567146

[22] A. Fogliata, G. Nicolini, A. Clivio, E. Vanetti and L. Cozzi, “Dosimetric Evaluation of Acuros XB Advanced Dose Calculation algorithm in heterogeneous media,” Radiation Oncology, Vol. 6, No. 82, 2011. doi:10.1186/1748-717X-6-82

[23] M. Kan, L. Leung and P. Yu, “Verification and Dosimetric Impact of Acuros XB Algorithm on Intensity Modulated Stereotactic Radiotherapy for Locally Persistent Nasopharyngeal Carcinoma,” Medical Physics, Vol. 39, No. 8, 2012, pp. 4705-4714. doi:10.1118/1.4736819

[24] T. Han, F. Mourtada, K. Kisling, J. Mikell, D. Followill and R. Howell, “Experimental Validation of Deterministic Acuros XB algorithm for IMRT and VMAT Dose Calculations with the Radiological Physics Center’s Head and Neck Phantom,” Medical Physics, Vol. 39, No. 4, 2012, Article ID: 2193. doi:10.1118/1.3692180

[25] L. Hoffmann, M. J?rgensen, L. Muren and J. Petersen, “Clinical Validation of the Acuros XB Photon Dose Calculation Algorithm, a Grid-Based Boltzmann Equation Solver,” Acta Oncologica, Vol. 51, No. 3, 2012, pp. 376385. doi:10.3109/0284186X.2011.629209

[26] A. Fogliata, G. Nicolini, A. Clivio, E. Vanetti and L. Cozzi, “On the Dosimetric Impact of Inhomogeneity Management In the Acuros XB Algorithm for Breast Treatment,” Radiation Oncology, Vol. 6, No. 103, 2011. doi:10.1186/1748-717X-6-103

[27] A. Fogliata, G. Nicolini, A. Clivio, E. Vanetti and L. Cozzi, “Critical Appraisal of Acuros XB and Anisotropic Analytic Algorithm Dose Calculation in Advanced NonSmall-Cell Lung Cancer Treatments,” International Journal of Radiation Oncology, Biology and Physics, Vol. 183, No. 5, 2012, pp. 1587-1595. doi:10.1016/j.ijrobp.2011.10.078

[28] L. Tillikainen, H. Helminen, T. Torsti, S. Siljam?ki, J. Alakuijala, J. Pyyry J and W. Ulmer, “3D Pencil-BeamBased Superposition Algorithm for Photon Dose Calculation in Heterogeneous Media,” Physics in Medicine and Biology, Vol. 53, No. 14, 2008, pp. 3821-3839. doi:10.1088/0031-9155/53/14/008

[29] I. Paddick I, “A simple Scoring Ratio to Index the Conformity of Radiosurgical Treatment Plans,” Technical Note, Journal of Neurosurgery, Vol. 93, No. 3, 2000, pp. 219-222.

[30] N. Papanikolaou, J. Battista, A. Boyer, C. Kappas, C. Klein, T. Mackie, M. Sharpe and J. Van Dyke, “Tissue Inhomogeneity Corrections for Megavoltage Photon Beams,” The American Association of Physicist in Medicine, College Park, 2004.

[31] C. Martens, N. Reynaert, C. De Wagter, P. Nilsson, M. Coghe, H. Palmans, H. Thierens and W. De Neve, “Underdosage of the Upper-Airway Mucosa for Small Fields as Used in Intensity-Modulated Radiation Therapy: A Comparison Between Radiochromic Film Measurements, Monte Carlo Simulations, and Collapsed Cone Convolution Calculations,” Medical Physics, Vol. 29, No. 7, 2002, pp. 1528-1535. doi:10.1118/1.1487421

[32] B. Vanderstraeten, N. Reynaert, L. Paelinck, I. Madani, C. De Wagter, W. De Gersem, W. De Neve and H. Thierens, “Accuracy of Patient Dose Calculation for Lung IMRT: A Comparison of Monte Carlo, Convolution/Superposition, and Pencil Beam Computations,” Medical Physics, Vol. 33, No. 9, 2006, pp. 3149-3158. doi:10.1118/1.2241992

[33] W. De Neve and C. De Wagter, “Lethal Pneumonitis in a Phase I Study of Chemotherapy and IMRT for NSCLC: the Need to Investigate the Accuracy of Dose Computation,” Radiotherapy Oncology, Vol. 75, No. 2, 2005, pp. 246-247. doi:10.1016/j.radonc.2005.03.024

[34] R. Kornelsen and M.Young, “Changes in the Dose-Profile of a 10 MV X-Ray Beam Within and Beyond Low Density Material,” Medical Physics, Vol. 9, No. 1, 1982, pp. 114-116. doi:10.1118/1.595059