The optimization problem of radiation intensity in radiation therapy

Document Type : Research Paper

Author

Master of Applied Mathematics, Isfahan University, Faculty of Science, Department of Mathematics Master of Industrial Management, Yazd University, Faculty of Economics, Management and Accounting, Department of Industrial Management

Abstract

Cancer is a disease that poses a serious threat to human health. It is the second leading cause of death in developing countries, with five out of every thousand people suffering from this disease. One of the effective methods in cancer treatment is radiation therapy. Radiation therapy aims to destroy the DNA of cancerous cells and prevent their growth and reproduction in other parts of the body using penetrating radiation. The key issue in this process is the precise number and intensity of the radiation beams. It is crucial to achieve the desired result while minimizing damage to healthy cells adjacent to the cancerous cells, which can be seen as a multi-objective optimization problem. In this article, we will present the formulated problem and examine the proposed algorithm to solve it.

Keywords


[1] H. P. Benson, An outcome space algorithm for optimization over the weakly efficient set of a multiple objective nonlinear programming problem, Global Optim., 52 (2012) 553–574.
[2] J. Brunke, K. Deb, K. Miettinen and R. Slowinski, Multiobjective Optimization, Springer-Verlag, Berlin, 2008.
[3] P. C. Chen, P. Hansen and B. Jaumard, On-line and off-Line vertex enumeration by adjacency lists, J. Oper. Res, 10 (1991) 403–409.
[4] M. Ehrgott and Sh. Lizhen, Approximately solving multiobjective linear programmes in objective space and an application in radiotherapy treatment planning, Math. Meth. Oper. Res., 68 (2008) 257–276.
[5] H. W. Hamacher and K. H. Kufer, Inverse radition therapy planning-a multiple objective optimization approach, Discrete-Appli Math., 118 (2002) 145–161.
[6] A. Holder, Designing radiotherapy plans with elastic constraints and interior point method, Health care management sci, 6 (2003) 5–16.
[7] A. J. Mundt and J. C. Roeske, Intensity Modulated Radiation Therapy: A Clinical Perspective, 1, Springer, Berlin, 1999.
[8] R. R. Roackafellar, Convex Analysis, Princeton University Press,Princeton, 1970.
[9] F. Verhaegen, Monto carlo modelling of extrenal radiotherapy photon beam, Phy. Med. Bio., 48 (2003) 107- -164.
[10] Lingo System, LINGO 9.0, Chicago, 2010.
Volume 1, Issue 4 - Serial Number 4
December 2016
Pages 31-49
  • Receive Date: 25 September 2015
  • Revise Date: 23 December 2015
  • Accept Date: 26 December 2015
  • Publish Date: 19 February 2017