Three Dimensional Expansion of Margins for Single-fraction Treatments: Stereotactic Radiosurgery Brain Cases

Affiliation(s)

Department of Medical Physics, Memorial Sloan Kettering Cancer Center, New York, NY 10065.

Department of Medical Physics, Memorial Sloan Kettering Cancer Center, New York, NY 10065.

ABSTRACT

**Purpose**: To derive a clinically-practical margin formula between clinical target volume (CTV) and planning target volume (PTV) for single-fraction stereotactic radiosurgery (SRS). **Methods**: In previous publications on the margin between the CTV and the PTV, a Gaussian function with zero mean was assumed for the systematic error and the machine systematic error was completely ignored. In this work we adopted a Dirac delta function for the machine systematic error for a given machine with nonzero mean systematic error. Mathematical formulas for calculating the CTV-PTV margin for single-fraction SRS treatments were proposed. **Results**: Margins for single fraction treatments were derived such that the CTVs received the prescribed dose in 95% of the SRS patients. The margin defined in this study was machine specific and accounted for nonzero mean systematic error. The differences between our formulas and a previously published formula were discussed. **Conclusion**: Clinical margin formulas were proposed for determining the margin between the CTV and the PTV in SRS treatments. Previous margin’s recipes, being derived specifically for conventional treatments, may be inappropriate for single-fraction SRS and could result in geometric miss of the target and even treatment failure for machines possessing of large systematic errors.

Cite this paper

Q. Zhang, M. Chan, Y. Song and C. Burman, "Three Dimensional Expansion of Margins for Single-fraction Treatments: Stereotactic Radiosurgery Brain Cases,"*International Journal of Medical Physics, Clinical Engineering and Radiation Oncology*, Vol. 1 No. 2, 2012, pp. 15-22. doi: 10.4236/ijmpcero.2012.12003.

Q. Zhang, M. Chan, Y. Song and C. Burman, "Three Dimensional Expansion of Margins for Single-fraction Treatments: Stereotactic Radiosurgery Brain Cases,"

References

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[10] D. Yan, J. Wong, F. Vicini, J. Michalski, C. Pan, A. Fra- zier, E. Horwitz and A. Martinez, “Adaptive Modification of Treatment Planning to Minimize the Deleterious Ef- fects of Treatment Setup Errors,” International Journal of Radiation Oncology, Biology and Physics, Vol. 38, No. 1, 1997, pp. 197-206. doi:10.1016/S0360-3016(97)00229-0

[11] O. A. Zeidan, K. M. Langen, S. L. Meeks, R. R. Manon, T. H. Wagner, T. R. Willoughby, D. W. Jenkins and P. A. Kupelian, “Evaluation of Image-Guidance Protocols in the Treatment of Head and Neck Cancers,” International Journal of Radiation Oncology, Biology and Physics, Vol. 67, No. 3, 2007, pp. 670-677. doi:10.1016/j.ijrobp.2006.09.040

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[13] T. Craig, J. Battista and J. Van Dyk, “Limitations of a Convolution Method for Modeling Geometric Uncertain- ties in Radiation Therapy: II. The Effect of a Finite Num- ber of Fractions,” Medical Physics, Vol. 30, No. 8, 2003, pp. 2012-2020. doi:10.1118/1.1589493

[14] M. G. Witte, J. van der Geer, C. Schneider, J. V. Lebesque and M. van Herk, “The Effects of Target Size and Tissue Density on the Minimum Margin Required for Random Errors,” Medical Physics, Vol. 31, No. 11, 2004, pp. 3068-3079. doi:10.1118/1.1809991

[15] S. F. Zavgorodni, “Treatment Planning Algorithm Cor- rections Accounting for Random Setup Uncertainties in Fractionated Stereotactic Radiotherapy,” Medical Physics, Vol. 27, No. 4, 2000, pp. 685-690. doi:10.1118/1.598930

[16] L. Masi, F. Casamassima, C. Polli, C. Menichelli, I. Bo- nucci and C. Cavedon, “Cone Beam CT Image Guidance for Intracranial Stereotactic Treatments: Comparison with a Frame Guided Set-Up,” International Journal of Radia- tion Oncology, Biology and Physics, Vol. 71, No. 3, 2008, pp. 926-933. doi:10.1016/j.ijrobp.2008.03.006

[17] Z. Wang, K. Wang, F. Lerma, B. Liu, P. Amin, B. Yi, G. Hobeika and C. Yu, “Planning Margins to CTV for Im-age-Guided Whole Pelvis Prostate Cancer Intensity- Modulated Radiotherapy,” International Journal of Medi-cal Physics, Clinical Engineering and Radiation Oncology, Vol. 1, No. 2, 2012, pp. 23-31.

[18] W. Du, J. N. Yang, E. L. Chang, D. Luo, M. F. McAleer, A. Shiu and M. K. Martel, “A Quality Assurance Proce- dure to Evaluate Cone-Beam CT Image Center Congru- ence with the Radiation Isocenter of a Linear Accelera- tor,” Journal of Applied Clinical Medical Physics, Vol. 11, No. 4, 2010, pp. 15-26.

[19] Q. Zhang, M. Chan, Y. Song, C. Burman and M. Zhang, “Three Dimensional Expansion of Margins for Single- Fraction Treatments: Stereotactic Radiosurgery Brain Cases,” In Preparation.

[1] C. C. Ling, Y. C. Lo and D. A. Larson, “Radiobiophysi- cal Aspects of Stereotaxic Radiation Treatment of Central Nervous System Diseases,” Seminars Radiation Oncol- ogy, Vol. 5, No. 3, 1995, pp. 192-196. doi:10.1016/S1053-4296(05)80016-5

[2] Y.-C. Lo, C. C. Ling and D. A. Larson, “The Effect of Setup Uncertainties on the Radiobiological Advantage of Fractionation in Stereotaxic Radiotherapy,” International Journal of Radiation Oncology, Biology and Physics, Vol. 34, No. 5, 1996, pp. 1113-1119. doi:10.1016/0360-3016(95)02179-5

[3] C. A. McBain, A. M. Henry, J. Sykes, A. Amer, T. Mar- chant, et al., “X-Ray Volumetric Imaging in Image-Guided Radiotherapy: The New Standard in On-Treatment Imag- ing,” International Journal of Radiation Oncology, Biology and Physics, Vol. 64, No. 2, 2006, pp. 625-634. doi:10.1016/j.ijrobp.2005.09.018

[4] A. Fukuda, “Pretreatment Setup Verification by Cone Beam CT in Stereotactic Radiosurgery: Phantom Study,” Journal of Applied Clinical Medical Physics, Vol. 11, No. 4, 2010, p. 3162.

[5] J. G. Zhu, “Feasibility of Using Cone-Beam CT to Verify and Reposition the Optically Guided Target Localization of Linear Accelerator Based Stereotactic Radiosurgery,” Medical Physics, Vol. 38, No. 1, 2011, pp. 390-396. doi:10.1118/1.3531547

[6] G. S. Mageras, Z. Fuks, S. A. Leibel, C. C. Ling, M. J. Zelefsky, et al., “Computerized Design of Target Mar- gins for Treatment Uncertainties in Conformal Radio- therapy,” International Journal of Radiation Oncology, Biology and Physics, Vol. 43, No. 2, 1999, pp. 437-445. doi:10.1016/S0360-3016(98)00386-1

[7] J. C. Stroom, H. C. J. de Boer, H. Huizenga and A. G. Visser,“ Inclusion of Geometrical Uncertainties in Ra- diotherapy Treatment Planning by Means of Coverage Probability,” International Journal of Radiation Oncol- ogy, Biology and Physics, Vol. 43, No. 4, 1999, pp. 905- 919. doi:10.1016/S0360-3016(98)00468-4

[8] M. van Herk, P. Remeijer, C. Rasch and J. V. Lebesque, “The Probability of Correct Target Dosage: Dose-Popu- lation Histograms for Deriving Treatment Margins in Ra- diotherapy,” International Journal of Radiation Oncology, Biology and Physics, Vol. 47, No. 4, 2000, pp. 1121-1135. doi:10.1016/S0360-3016(00)00518-6

[9] D. Yan, D. Lockman, A. Martinez, J. Wong, D. Brabbins, F. Vicini, J. Liang, and L. Kestin, “Computed Tomogra- phy Guided Management of Interfractional Patient Varia- tion,” Seminars in Radiation Oncology, Vol. 15, No. 3, 2000, pp. 168-179. doi:10.1016/j.semradonc.2005.01.007

[10] D. Yan, J. Wong, F. Vicini, J. Michalski, C. Pan, A. Fra- zier, E. Horwitz and A. Martinez, “Adaptive Modification of Treatment Planning to Minimize the Deleterious Ef- fects of Treatment Setup Errors,” International Journal of Radiation Oncology, Biology and Physics, Vol. 38, No. 1, 1997, pp. 197-206. doi:10.1016/S0360-3016(97)00229-0

[11] O. A. Zeidan, K. M. Langen, S. L. Meeks, R. R. Manon, T. H. Wagner, T. R. Willoughby, D. W. Jenkins and P. A. Kupelian, “Evaluation of Image-Guidance Protocols in the Treatment of Head and Neck Cancers,” International Journal of Radiation Oncology, Biology and Physics, Vol. 67, No. 3, 2007, pp. 670-677. doi:10.1016/j.ijrobp.2006.09.040

[12] T. Craig, J. Battista and J. Van Dyk,“ Limitations of a Convolution Method for Modeling Geometric Uncertain-ties in Radiation Therapy: I. The Effects of Shift Invari-ance,” Medical Physics, Vol. 30, No. 8, 2003, pp. 2001- 2011. doi:10.1118/1.1589492

[13] T. Craig, J. Battista and J. Van Dyk, “Limitations of a Convolution Method for Modeling Geometric Uncertain- ties in Radiation Therapy: II. The Effect of a Finite Num- ber of Fractions,” Medical Physics, Vol. 30, No. 8, 2003, pp. 2012-2020. doi:10.1118/1.1589493

[14] M. G. Witte, J. van der Geer, C. Schneider, J. V. Lebesque and M. van Herk, “The Effects of Target Size and Tissue Density on the Minimum Margin Required for Random Errors,” Medical Physics, Vol. 31, No. 11, 2004, pp. 3068-3079. doi:10.1118/1.1809991

[15] S. F. Zavgorodni, “Treatment Planning Algorithm Cor- rections Accounting for Random Setup Uncertainties in Fractionated Stereotactic Radiotherapy,” Medical Physics, Vol. 27, No. 4, 2000, pp. 685-690. doi:10.1118/1.598930

[16] L. Masi, F. Casamassima, C. Polli, C. Menichelli, I. Bo- nucci and C. Cavedon, “Cone Beam CT Image Guidance for Intracranial Stereotactic Treatments: Comparison with a Frame Guided Set-Up,” International Journal of Radia- tion Oncology, Biology and Physics, Vol. 71, No. 3, 2008, pp. 926-933. doi:10.1016/j.ijrobp.2008.03.006

[17] Z. Wang, K. Wang, F. Lerma, B. Liu, P. Amin, B. Yi, G. Hobeika and C. Yu, “Planning Margins to CTV for Im-age-Guided Whole Pelvis Prostate Cancer Intensity- Modulated Radiotherapy,” International Journal of Medi-cal Physics, Clinical Engineering and Radiation Oncology, Vol. 1, No. 2, 2012, pp. 23-31.

[18] W. Du, J. N. Yang, E. L. Chang, D. Luo, M. F. McAleer, A. Shiu and M. K. Martel, “A Quality Assurance Proce- dure to Evaluate Cone-Beam CT Image Center Congru- ence with the Radiation Isocenter of a Linear Accelera- tor,” Journal of Applied Clinical Medical Physics, Vol. 11, No. 4, 2010, pp. 15-26.

[19] Q. Zhang, M. Chan, Y. Song, C. Burman and M. Zhang, “Three Dimensional Expansion of Margins for Single- Fraction Treatments: Stereotactic Radiosurgery Brain Cases,” In Preparation.