放射療法是目前最常見的一種癌症治療方式，而強度調控放射治療 (Intensity Modulated Radiation Therapy, IMRT)是放射療法目前新發展的技術。強度調控放射治療最大的好處，就是能夠有效地調節放射出的劑量，將高劑量集中於腫瘤部位，同時降低治療期間對周邊正常組織的傷害。
「多葉準直儀 (Multileaf Collimator, MLC)」是執行強度調控放射治療必備的醫療器材之一，它是由許多對葉扇組成，藉由一連串複雜的葉扇移動，來達到強度調控放射治療的目的。儘管好多年前，就已經有學者開始研究放射線醫療相關的技術與設備，但在「多葉準直儀的移動效率」方面，仍有許多可以改善的空間。對於一個放射治療計畫而言，如果放射線傳送時間(Total Delivery Time)太長，不但會影響醫療的品質，也會造成病人不舒適。而影響放射線傳送時間最主要的三個因子，分別為：監控數(Monitor Units, MUs)、分割數(Segments)、及葉扇移動距離。
本論文發展一個「三階段的混合整數規劃」來達成最短放射線傳送時間。首先最小化監控數；然後在最小監控數的條件下最小化分割數；最後在最小監控數以及分割數的條件下，最小化葉扇移動距離。實驗結果證明我們所提出的方法相較於先前文獻所提出的方法有明顯的改善。

Radiation therapy is a common treatment for some specific tumors in the treatment of cancer now. In recent years, there has been a new development in radiation therapy, which is called intensity modulated radiation therapy (IMRT). The outstanding advantage of IMRT is it can modulate the intensity of the radiation beam effectively, and focus a higher radiation dose on the tumor while minimizing radiation exposure to surrounding normal tissues.
Multileaf Collimator (MLC) is one of the essential equipments when IMRT is executed. MLC is composed by several pairs of leaves, and it can achieve the objective of intensity modulated by series moving of leaves. Although the medical radiation therapy has been studied for a long time, the efficiency of MLC operations can be further improved. For a radiation therapy plan, a long total delivery time may not only diminish the quality of therapy but also cause uncomfortable perception to a patient. Three criteria which effect total delivery time are number of monitor units (MUs), number of segments, and distance of leaf traveled.
This study aims to develop a three-stage-optimization algorithm to achieve a shortest total delivery time. We minimize the number of monitor units at first. Then we minimize the number of segments with minimum number of monitor units. Finally, we try to shorten the distance of leaf traveled when minimum number of monitor units and segments are used. According to the outcomes of series of experiments, we show that the performance of our algorithm is better than previous works significantly to solve a radiation therapy plan.

[1] 林口長庚放射腫瘤科,http://www.cgmh.com.tw/intr/intr2/c33e0/
[2] 厚生腫瘤中心,http://www.toa365.com.tw/
[3] 行政院衛生署衛生統計資訊網,http://www.doh.gov.tw/statistic/
[4] Ahuja, R. K. and H. W. Hamacher, “A network flow algorithm to minimize beam-on time for unconstrained multileaf collimator problems in cancer radiation therapy.” NETWORKS, 45 (1), 36-41, (2005)
[5] Bednarz, G., D. Michalski, C. Houser, M. S. Huq, Y. Xiao, P. R. Anne, and J. M. Galvin, “The use of mixed-integer programming for inverse treatment planning with pre-defined field segments.” PHYSICS IN MEDICINE AND BIOLOGY, 47 (13), 2235-2245, (2002)
[6] Boland, N., H. W. Hamacher, and F. Lenzen, “Minimizing beam-on time in cancer radiation treatment using multileaf collimators.” NETWORKS, 43 (4), 226-240, (2004)
[7] Bortfeld, T. R., D. L. Kahler, and T. J. Waldron, and A.L. Boyer, “X-ray field compensation with multileaf collimators.” INTERNATIONAL JOURNAL OF RADIATION ONCOLOGY BIOLOGY PHYSICS, 28 (3), 723-730, (1994)
[8] Chen, Y., Q. Hou, and J. M. Galvin, “A graph-searching method for MLC leaf sequencing under constraints.” MEDICAL PHYSICS, 31 (6), 1504-1511, (2004)
[9] Convery, D. J., and M. E. Rosenbloom “The generation of intensity-modulated fields for conformal radiotherapy by dynamic collimation.” PHYSICS IN MEDICINE AND BIOLOGY, 37 (6), 1359-1374, (1992)
[10] Craft, D., P. Suss, and T. Bortfeld, “The tradeoff between treatment plan quality and required number of monitor units in intensity-modulated radiotherapy.” INTERNATIONAL JOURNAL OF RADIATION ONCOLOGY BIOLOGY PHYSICS, 67 (5), 1596-1605, (2007)
[11] Dai, J. R., and Y. P. Zhu, “Minimizing the number of segments in a delivery sequence for intensity-modulated radiation therapy with a multileaf collimator.” MEDICAL PHYSICS, 28 (10), 2113-2120, (2001)
[12] Dai, J. R., and W. Que, “Simultaneous minimization of leaf travel distance and tongue-and-groove effect for segmental intensity-modulated radiation therapy.” PHYSICS IN MEDICINE AND BIOLOGY, 49 (23), 5319-5331, (2004)
[13] Dou, X., X. D.Wu, J. E. Bayouth, and J. M. Buatti, “The matrix orthogonal decomposition problem in intensity-modulated radiation therapy.” LECTURE NOTES IN COMPUTER SCIENCE, 4112, 156-165 (2006)
[14] Galvin, J. M., X. G. Chen, and R. M. Smith, “Combining multileaf fields to modulate fluence distributions.” INTERNATIONAL JOURNAL OF RADIATION ONCOLOGY BIOLOGY PHYSICS, 27 (3), 697-705, (1993)
[15] Kalinowski, T., “Reducing the number of monitor units in multileaf collimator field segmentation.” PHYSICS IN MEDICINE AND BIOLOGY, 50 (6), 1147-1161, (2005)
[16] Kallman, P., B. Lind, A. Eklof, and A. Brahme, “Shaping of arbitrary dose distributions by dynamic multileaf collimation.” PHYSICS IN MEDICINE AND BIOLOGY, 33 (11), 1291-1300, (1988)
[17] Lin, K. H., Huang Sheng-Sang, Liu Mu-Tai, Lin Jao-Perng, and Tsai Song-Su, “Clinical Applications and Dosimetric Characteristics of Multi-leaf Collimator in Intensity Modulated Radiation Therapy.” THE CHANGHUA JOURNAL OF MEDICINE, 8 (1), 13-20, (2003)
[18] Langer, M., V. Thai, and L. Papiez, “Improved leaf sequencing reduces segments or monitor units needed to deliver IMRT using multileaf collimators.” MEDICAL PHYSICS, 28 (12), 2450-2458, (2001)
[19] Lenzen, F., “An integer programming approach to the multileaf collimator problem.” DIPLOMA THESIS DEPARTMENT OF MATHEMATICS, UNIVERSITY OF KAISERSLAUTERN, GERMANY, (2000)
[20] Li, K. L., J. R. Dai, and L. J. Ma, “Simultaneous minimizing monitor units and number of segments without leaf end abutment for segmental intensity modulated radiation therapy delivery.” MEDICAL PHYSICS, 31 (3), 507-512, (2004)
[21] Matsumoto, S., H. L. Kundel, G. C. James, W. B. Gefter, and H. Hatabu, “Pulmonary nodule detection in CT images with quantized convergence index filter.” MEDICAL IMAGE ANALYSIS , 10 (3), 343-352, (2006)
[22] Que, W., “Comparison of algorithms for multileaf collimator field segmentation.” MEDICAL PHYSICS, 26 (11), 2390-2396, (1999)
[23] 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)
[24] Siochi, R. A. C, “Minimizing static intensity modulation delivery time using an intensity solid paradigm.” INTERNATIONAL JOURNAL OF RADIATION ONCOLOGY BIOLOGY PHYSICS, 43 (3), 671-680, (1999)
[25] Spirou, S. V., and C. S. Chui, “Generation of arbitrary intensity profiles by dynamic jaws or multileaf collimators.” MEDICAL PHYSICS, 21 (7), 1031-1041, (1994)
[26] Van Santvoort, J. P. C., and B. J. M. Heijmen, “Dynamic multileaf collimation without 'tongue-and-groove' underdosage effects.” PHYSICS IN MEDICINE AND BIOLOGY, 41 (10), 2091-2105, (1996)
[27] Wang, C., J. R. Dai, and Y. M. Hu, “Optimization of beam orientations and beam weights for conformal radiotherapy using mixed integer programming” PHYSICS IN MEDICINE AND BIOLOGY, 48 (24), 4065-4076, (2003)
[28] Xia, P., J. Y. Ting, and C. G.. Orton, “Segmental MLC is superior to dynamic MLC for IMRT delivery.” MEDICAL PHYSICS, 34 (7), 2673-2675, (2007)
[29] Xia, P., and L. J. Verhey, “Multileaf collimator leaf sequencing algorithm for intensity modulated beams with multiple static segments.” MEDICAL PHYSICS, 25 (8), 1424-1434, (1998)
[30] Xing, L., R. J. Hamilton, C. Pelizzari, and G. T. Y. Chen, “A three-dimensional algorithm for optimizing beam weights and wedge filters.” MEDICAL PHYSICS, 25 (10), 1858-1865, (1998)
[31] Yang, R., J. Dai, Y. Yang, and Y. Hu, “Beam orientation optimization for intensity-modulated radiation therapy using mixed integer programming.” PHYSICS IN MEDICINE AND BIOLOGY, 51 (15), 3653-3666, (2006)