Radiotherapy Treatment Design and Linear Programming
Intensity modulated radiotherapy treatment (IMRT) design is the process of choosing how beams of radiation will travel through a cancer patient to treat the disease, and although optimization techniques have been suggested since the 1960s, they are still not widely used. Instead, the vast majority of treatment plans are designed by clinicians through trial-and-error. Modern treatment facilities have the technology to treat patients with extremely complicated plans, and designing plans that take full advantage of the technology is tedious. The increased technology found in modern treatment facilities makes the use of optimization paramount in the design of successful treatment plans. The goals of this work are to 1) present a concise description of the linear models that are under current investigation, 2) develop the analysis certificates that these models allow, and 3) suggest future research avenues.
Key wordsMathematical programming Intensity modulated radiotherapy treatment
Unable to display preview. Download preview PDF.
- Censor, Y. (1991). Mathematical aspects of radiation therapy treatment planning: Continuous inversion versus full discretization and optimization versus feasibility. In Borgers, C. and F. Natterer, Eds., Computational Radiology and Imaging: Therapy and Diagnostic. Springer-Verlag, New York, NY, 101–112.Google Scholar
- Goitein, M. and A. Niemierko (1988). Biologically based models for scoring treatment plans. Scandinavian Symposium on Future Directions of Computer-Aided Radiotherapy.Google Scholar
- Withers, H., J. Taylor, and B. Maciejewski (1987). Treatment volume and tissue tolerance. International Journal of Radiation Oncology, Biology, Physics, 14, 751–759.Google Scholar
- Ferris, M. and M. Voellker (2002). Neuro-dynamic programming for radiation treatment planning. Technical Report NA-02/06, Numerical Analysis Group, Computing Laboratory, Oxford University.Google Scholar
- Boland, N., H. Hamacher, and F. Lenzen (2002). Minimizing beam-on time in cancer radiation treatment using multileaf collimators. Technical Report KLUEDO: 2002-02-10, Universittsbibliothek Kaiserslautern.Google Scholar
- Holder, A. (2001). Partitioning multiple objective solutions with applications in radiotherapy design. Technical Report 54, Department of Mathematics, Trinity University, San Antonio, TX.Google Scholar
- Lodwick, W., S. McCourt, F. Newman, and S. Humphries (1998). Optimization methods for radiation therapy plans. In Borgers, C. and F. Natterer, Eds., Computational, Radiology and Imaging: Therapy and Diagnosis. Springer-Verlag, New York, NY.Google Scholar
- Berman, A. and R. Plemmons (1979). Nonnegative Matrices in the Mathematical Sciences. Academic Press, New York, NY.Google Scholar
- Roos, C., T. Terlaky, and J.-P. Vial (1997). Theory and Algorithms for Linear Optimization: An Interior Point Approach. John Wiley and Sons, New York, NY.Google Scholar