放射線療法為常見的癌症治療方式。強度調控放射治療(Intensity Modulated Radiation Therapy, IMRT)是近年以來新發展的技術，它可以藉由調節射束強度，將高劑量集中在癌細胞上，並且同時減少周圍組織的劑量。IMRT治療計畫的優劣取決於射束方向及其射束強度，然而，在目前的放射治療中，最適射束角度的選取是依據治療物理師的經驗及直覺。
為了提供治療物理師最佳化治療計畫、減少計算時間及增加治療品質，本論文首先以分割方法去計算在每個voxel中，從不同射束角度所累積的劑量，然後使用混合整數規劃方法同時最佳化射束角度及其強度，另外，我們也將劑量-體積及臨床上不選取對角的經驗加入限制式。最後，與目前最佳化治療計畫進行比較，實驗結果證明本研究所提出的方法於重要器官所接收到的劑量及計算時間皆有明顯的改善。

Currently, radiation therapy is a common treatment for some specific tumors in the treatments of cancer. Intensity modulated radiation therapy (IMRT) is a widely adopted new radiation therapy tool in recently years, which can deliver high radiation doses to the tumor while reducing sparing of surrounding normal tissues by modulate radiation intensity across beams. The optimal IMRT treatment planning depends on the collection of directions and corresponding intensities. However, in current practice of IMRT, beam angle selection is accomplished by a trial-and-error approach based on the treatment planner’s experience or intuition.
In this thesis, in order to assist the planner to optimize IMRT treatment planning efficiently, reduce the computational time and improve the quality of the treatment, we code a program to pre-calculate the radiation dose in each voxel by the form of discretization. We then present a mathematical model to optimize beam angle and fluence map simultaneously by mixed integer programming approach. In addition, we consider the practical experience of the planner and dose-volume constraints in the proposed model to improve the quality of the treatment. According to the results of the experiment, we show that the performance of our method to solve IMRT treatment planning is better than previous works in decreasing radiation dose of organs at risk and computational time.

[1] 行政院衛生署衛生統計資訊網，2009。取自http://www.doh.gov.tw/statistic/。
[2] American College of Radiology (ACR). ACR Practice Guideline for Intensity Modulated Radiation Therapy. 2007 (Res. 17). ACR Practice Guideline. Reston, Accessed 2009. Available at: http://www.acr.org/SecondaryMainMenuCategories/quality_safety/guidelines/ro/imrt.aspx.
[3] Attix, F.H., “Introduction to Radiological Physics and Radiation Dosimetry”, Wiley, New York (1986).
[4] Bär, W., Schwarz, M. and Alber M., Bos, L.J., Mijnheer, B.J., Rasch, C., Schneider, C., Nusslin, F., Damen, E.M.F., “A comparison of forward and inverse treatment planning for intensity-modulated radiotherapy of head and neck cancer”, Radiother Oncol, 69, 251-258 (2003).
[5] Bortfeld, T., “ IMRT: a review and preview”, Phys. Med. Biol. 51, 363-379 (2006).
[6] Cedric, X.Y., Christopher, J.A., Michelle, S., “Planning and delivery of intensity-modulated radiation therapy”, Med. Phys, 35(12), 5233-5241 (2008).
[7] David, C., “Local beam angle optimization with linear programming and gradient search”, Phys Med Biol, 52(7), N127-N135 (2007).
[8] Djajaputra, D., Wu, Q., Wu, Y., Mohan, R., “Algorithm and performance of a clinical IMRT beam-angle optimization system”, Phys Med Biol, 48(19), 3191-3212 (2003).
[9] Ehrgott, M., Güler, Ç., Hamacher, H.W., and Shao, L., “Mathematical optimization in intensity modulated radiation therapy”, 4OR: A Quarterly Journal of Operations Research, 6(3), 199-262 (2008).
[10] Ezzell, G.A., Galvin, J.M., Low, D., “Guidance document on deliver, treatment planning, and clinical implementation of IMRT: Report of the IMRT subcommittee of the AAPM radiation therapy committee”, Med. Phys, 30, 2089-2115 (2003).
[11] Grigorov, G. N., Chow, J. C., Grigorov, L., Jing, R. and Barnett, R. B., “IMRT: Improvement in treatment planning efficiency using NTCP calculation independent of the dose-volume-histogram”, Med. Phys, 33, 1250-1258 (2006).
[12] Hamacher, H.W., and Küfer, K.H. “Inverse radiation therapy planning – a multiple objective optimization approach”, Discrete Applied Mathematics, 118, 145-161 (2002).
[13] Lee, E. Fox, T., Crocker, I., “Integer programming applied to intensity-modulated radiation therapy treatment planning”, Ann Oper Res, 119, 165-181 (2003).
[14] Lee, E.K., Fox, T., Crocker, I., “ Simultaneous beam geometry and intensity map optimization in intensity-modulated radiation therapy”, Int J Radiat Oncol Biol Phys, 64, 301-320 (2006).
[15] Li, Y., Yao, J. and Yao, D., “Automatic beam angle selection in IMRT planning using genetic algorithm”, Phys Med Biol, 49, 1915-1932 (2004).
[16] Lim, G.J., Choi, J., and Mohan, R., "Iterative Solution methods for Beam Angle and Fluence Map Optimization in IMRT”, OR Spectr, 30(2), 289-309 (2008).
[17] Lim, G.J., Choi, J., Mohan, R., “Iterative solution methods for beam angle and fluence map optimization in intensity modulated radiation therapy planning”, OR Spectr, 30, 289-309 (2008).
[18] Pugachev, A and Xing, L., “Computer-assisted selection of coplanar beam orientation in intensity-modulated radiation”, Phys Med Biol, 46, 2467-2476 (2001).
[19] Pugachev, A and Xing, L., “Incorporating prior knowledge into beam orientation optimization in IMRT”, Int J Radiat Oncol Biol Phys, 54, 1565-1574 (2002).
[20] Pugachev, A., Li, M.S., Boyer, A.L., Hancock, S.L., Le, Q.T., “Role of beam orientation optimization in intensity-modulated radiation therapy”, Int J Radiat Oncol Biol Phys, 50(2), 551-560 (2001).
[21] Romeijn, H.E., Ahuja, R.K., Dempsey, J.F., Kumar, A. and Li, J.G., “A novel linear programming approach to fluence map optimization for intensity modulated radiation therapy treatment planning”, Phys Med Biol, 48, 3521-3542 (2003).
[22] Shepard, D.M., Ferris, M.C., Olivera, G.M. and Mackie T.R., “Optimizing the Delivery of Radiation Therapy to Cancer Patients”, SIAM Rev., 41(4), 721-744 (1999).
[23] Stein, J., Mohan, R., Wang, X.H., Bortfeld, T., Wu, Q., Preiser, K., Ling, C. and Schlegel, W., “Number and orientations of beams in intensity-modulated radiation treatments”, Med. Phys, 24, 149-160 (1997).
[24] Thomas, E., Chapet, O., Kessler, M.L., Lawrence, T.S. and Haken, R.K., “Benefit of using biologic parameters (EUD and NTCP) in IMRT optimization for treatment of intrahepatic tumors”, Int J Radiat Oncol Biol Phys, 62, 571–578 (2005).
[25] Wang, C., Dai, J., Hu, Y., “Optimization of beam orientations and beam weights for conformal radiotherapy using mixed integer programming”, Phys Med Biol, 48, 4065-4076 (2003).
[26] Wang, X.C., Zhang, X.D. and Dong, L. et al., “Development of methods for beam angle optimization for IMRT using an accelerated exhaustive search strategy”, Int J Radiat Oncol Biol Phys, 60, 1325–1337 (2004).
[27] Webb, S., “Optimization of conformal radiotherapy dose distributions by simulated annealing”, Phys Med Biol, 34, 1349-1370 (1989).
[28] Wu,.V.W. Sham, J.S. and Kwong, D.L., “Inverse planning in three-dimensional conformal and intensity-modulated radiotherapy of mid-thoracic oesophageal cancer”, Br J Radiol, 77, 568-572 (2004).
[29] Yang, R., Dai, J., Yang, Y. and Hu, Y., “Beam orientation optimization for intensity-modulated radiation therapy using mixed integer programming”, Phys Med Biol, 51, 3653-3666 (2006).
[30] Yu, R. S., “Optimal Selection of Beam Orientations in Intensity Modulated Radiation Therapy”, Diploma Thesis Department of Industrial Engineering and Engineering Management, National Tsing Hua University, Taiwan (2006).