A bi-objective optimization model for planning the treatment of cancer cells by volumetric modulated arc therapy

Document Type : Industry Article

Author

Abstract

Cancer, one of the leading causes of death in the world, has been on the rise in recent years and is expected to continue in the coming years. Therefore, the importance of developing a cancer control program and the need to provide effective methods is very important. Given that radiation therapy is an effective way to treat cancer, studies on this method of treatment are important and significant. The main purpose of this paper is to provide a mathematical model for the latest method of radiotherapy called volumetric modulated arc therapy. In most studies in this field, due to the complexity of the model, the purpose of the problem is to maximize the dose received in the target area or to minimize the dose received in the area organs at risk. In this study, both objectives are considered together and a bi-objective model is presented. The results of the 8 studied instances show that the dose received in the target area is significantly higher than the dose received in the area around the tumor. In addition to increasing the dose received in the target area and decreasing the dose received in the cells around the target, the distribution of the dose in the voxels is very important, so the dose was examined with the coefficient of variation. The results show that the proposed model with a coefficient of variation of less than 10% has a conformal dose distribution in all tissues (cancerous tissue and healthy tissue).

Keywords

References

 
[1] J.C. Cheng, K.S. Chao and D. Low, "Comparison of intensity modulated radiation therapy (IMRT) treatment techniques for nasopharyngeal carcinoma", International Journal of Cancer, Vol. 96, No. 2, 2001, pp. 126-32.
[2] Z. Taheri‐Kadkhoda, N. Pettersson, T. Bjork‐Eriksson et al., "Superiority of intensity‐modulated radiotherapy over three‐dimensional conformal radiotherapy combined with brachytherapy in nasopharyngeal carcinoma: a planning study", The British Journal of Radiology, Vol. 81, No. 965, 2008, pp. 397-405.
[3] K. Akartunalı, V. Mak-Hau and T. Tran, "A unified mixed-integer programming model for simultaneous fluence weight and aperture optimization in VMAT, Tomotherapy, and Cyberknife", Computers & Operations Research, Vol. 56, 2015, pp. 134-150.
[4] H.O. Gozbasi, "Optimization approaches for planning external beam radiotherapy", PhD dissertation, Georgia Institute of Technology, 2010.
[5] P. Dursun, Z.C. Taşkın and İ.K. Altınel, "Mathematical Models for Optimal Volumetric Modulated Arc Therapy (VMAT) Treatment Planning", Procedia Computer Science, Vol. 100, 2016, pp. 644-651.
[6] F. Peng, S.B. Jiang, H.E. Romeijn and M.A. Epelman, "VMATc: VMAT with constant gantry speed and dose rate", Physics in Medicine & Biology, Vol. 60, No. 7, 2015, pp. 29-55
[7] F. Peng, "Optimization Methods for Volumetric Modulated Arc Therapy and Radiation Therapy under Uncertainty", Doctoral dissertation, University of Michigan, 2013.
[8] K. Akartunalı and V. Mak-Hau, "Treatment planning optimization for volumetric-modulated arc therapy (VMAT): Heuristic approaches", Optimization, 2012.
[9] B. Sun, Z. Shi, J. Song, G. Zhu and L. Shi, "A linearized model and nested-partitions heuristics for VMAT radiation treatment planning optimization", IEEE International Conference on Automation Science and Engineering (CASE), 2013, pp. 629-633.
[10] B. Sun, J. Song, G. Zhu and L. Shi, "A two-stage approach for VMAT treatment plan optimization", IEEE International Conference on Automation Science and Engineering (CASE), 2013, pp. 455-460.
[11] F. Peng, X. Jia, X. Gu, M.A. Epelman, H.E. Romeijn and S.B. Jiang, "A new column-generation-based algorithm for VMAT treatment plan optimization", Physics in Medicine & Biology, Vol. 57, No. 14, 2012, pp. 45-69.
[12] Y. Yang, B. Dong and Z. Wen, "Randomized algorithms for high quality treatment planning in volumetric modulated arc therapy", Inverse Problems, Vol. 33, No. 2, 2017, pp. 22 – 42.
[13] M. Teoh, C. Clark, K. Wood, S. Whitaker and A. Nisbet, "Volumetric modulated arc therapy: a review of current literature and clinical use in practice", The British journal of radiology, Vol. 84, No. 1007, pp. 967-996.
[14] J. Song, Z. Shi, B. Sun and L. Shi, "Treatment planning for volumetric-modulated arc therapy: Model and heuristic algorithms", IEEE Transactions on Automation Science and Engineering, Vol. 12, No. 1, 2014, pp. 116-126.
[15] P. Dursun, Z.C. Taşkın and İ.K. Altınel, "The determination of optimal treatment plans for Volumetric Modulated Arc Therapy (VMAT)", European Journal of Operational Research, Vol. 272, No. 1, 2019, pp. 372-388.
[16] P. Dursun, Z.C. Taşkın and İ.K. Altınel, "Using branch-and-price to determine optimal treatment plans for volumetric modulated arc therapy (VMAT)", Computers & Operations Research, Vol. 110, No. 1, pp. 1-17.
[۱۷] مائده رحیم‌نژاد، بهمن وحیدی، بهمن ابراهیمی حسین‌زاده و فاطمه یزدیان، «شبیه‌سازی دینامیک مولکولی برهم‌کنش داروی ضدّ سرطان پاکلیتاکسل با غشای سلّولی: بررسی تغییرات انرژی واندروالسی و فاصلة مرکز جرم»، مجلة مدل‌سازی در مهندسی، دورة ۱۷، شمارة ۵۷، تابستان 1398، صفحة 15-25.
[۱۸] یوسف بیناباجی و بهمن وحیدی، «تحلیل عددی اثر تغییرات شتاب گرانشی بر نشست ذرّات معلّق در مسیرهای هوایی نای-برونشی انسان: شبیه‌سازی محاسباتی سه‌بعدی»، مجلة مدل‌سازی در مهندسی، دورة ۱۷، شمارة ۵۹، زمستان 1398، صفحة 109-128.
[۱۹] امین رضایی‌پناه، علی مبارکی و سعید بحرانی خادمی، «بهینه‌سازی شبکة عصبی MLP با استفاده از الگوریتم ژنتیک موازی FinGrain برای تشخیص سرطان سینه»، مجلة مدل‌سازی در مهندسی، دورة ۱۷، شمارة ۵۷، تابستان 1398، صفحة ۱۸۶-۱۷۳.
[20] W.L. Winston and J.B. Goldberg, Operations Research: Applications and Algorithms, Thomson Brooks/Cole, 2004.
[21] G. Bahr, J. Kereiakes, H. Horwitz, R. Finney, J. Galvin and K. Goode, "The method of linear programming applied to radiation treatment planning", Radiology, Vol. 91, No. 4, 1968, pp. 686-693.
[22] D. Craft, M., Bangert, T. Long, D. Papp and J. Unkelbach, "Shared data for intensity modulated radiation therapy (IMRT) optimization research: the CORT dataset", GigaScience, Vol. 3, No. 1, 2014, pp. 2047-217X-3-37.
 
 
 
 
 
 
Journal of Modeling in Engineering
Volume 19, Issue 64
April 2021
Pages 95-107

Files

History

  • Receive Date: 11 August 2020
  • Revise Date: 18 November 2020
  • Accept Date: 20 December 2020

Share

How to cite

Statistics