Abstract
Brachytherapy (brachy being derived from a Greek word meaning short) is the treatment by means of radioactive sources that are placed at short distances from the target cells. This form of therapy is becoming common in the treatment of early stage prostate cancer, the most common cancer and the second leading cause of cancer deaths among American males. We consider the use of mixed-integer programming (MIP) models and branch-and-bound (BB) methods to optimize the placement within the prostate of the radioactive “seeds” used in this procedure. Several different optimization models are considered along with a number of branchand- bound strategies. With appropriate combinations of modelling and solution strategies, nearoptimal seed placements can be generated for each two-dimensional ultrasound section of the prostate in less than five minutes on a 333-MHz workstation. The original three-dimensional problem can then be solved by considering an appropriately interrelated sequence of these two-dimensional problems.
Similar content being viewed by others
References
AAPM Report No. 21, Recommendations of AAPM Task Group 32: Specification of Brachytherapy Source Strength (American Institute of Physics, New York, 1987).
Biomedical Business International Newsletter (1996), 72–75.
Blasko, J.C., Ragde, H., Schumacher, D. (1987), Transperineal percutaneous iodine-125 implantation for prostatic carcinoma using transrectal ultrasound and template guidance, Endocurie. Hypertherim. Oncol. 131–139.
Blasko, J.C., Wallner, K. (1997), Brachytherapy alone for early stage prostate cancer – Part I: Patient selection and technique (39th Annual Meeting, American Society for Therapeutic Radiology and Oncology, Orlando, FL.)
Brahme, A. (1995), Treatment optimization using physical and radiobiological objective functions. In: Smith, A.R. (ed.), Radiation Therapy Physics, Springer, New York, pp. 209–246.
Brooke, A., Kendrick, D., Meeraus, A., Raman, R. (1997), GAMS: A User's Guide. The Scientific Press, San Francisco, CA.
D'Souza, W.D., Meyer, R., Thomadsen, B.R. and Ferris, M.C. (2001), An iterative sequential mixed-integer approach to automated prostate brachytherapy treatment optimization, Physics in Medicine and Biology 46, 297–322.
Ezzell, G.A. (1996), Genetic and geometric optimization of three-dimensional radiation planning, Medical Physics, 293–305.
Ferris, M.C. (1998), MATLAB and GAMS: Interfacing Optimization and Visualization Software, Mathematical Programming Technical Report 98-19, Computer Sciences Department, University of Wisconsin-Madison, WI.
Gallagher, R.J. and Lee, E.K. (1997), Mixed integer programming optimization models for brachytherapy treatment planning. Proceedings/AMIA Annual Fall Symposium, 278–282.
Grimm, P.D., Blasko, J.C. and Ragde, H. (1994), Ultrasound-guided transperineal implantation of iodine-125 and palladium-103 for the treatment of early stage prostate cancer, Atlas Urol. Clin. North Am. 113–125.
Hole, J.H. Jr. (1993), Human Anatomy and Physiology, Ch. 22. Wm.C. Brown, Dubuque, IA.
Lee, E.K., Gallagher, R.J., Silvern, D., Wuu, C.S. and Zaider, M. (1999), Treatment planning for brachytherapy: an integer programming model, two computational approaches and experiments with permanent prostate implant planning, Phys. Med. Biol. 145–165.
Nath, R. (1995), Physical properties and clinical uses of brachytherapy radionuclides. In: Williamson, J.F., Thomadsen, B.R. and Nath, R. (eds.), Brachytherapy Physics, pp. 7–37. Medical Physics Publishing, Madison, WI.
Nath, R., Anderson, L.L., Weaver, K.A., Williamson, J.F. and Meigooni, A.S. (1995), Dosimetry of interstitial brachytherapy sources: recommendations of the AAPM Radiation Therapy Committee Task Group No. 43, Medical Physics 209–233.
Pouliot, J., Tremblay, D., Roy, J. and Felice, S. (1996), Optimization of permanent 125I prostate implants using fast simulated annealing, Int. J. Rad. Oncol. Biol. Phys. 711–720.
Yang, G., Reinstein, L.E., Pai, S. and Xu, Z. (1998), A new algorithm technique in optimization of permanent 125I prostate implants, Medical Physics 2308–2315.
Yu, Y. and Schell, M.C. (1996), A genetic algorithm for the optimization of prostate implants, Medical Physics 2085–2091.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Meyer, R.R., D'Souza, W.D., Ferris, M.C. et al. MIP Models and BB Strategies in Brachytherapy Treatment Optimization. Journal of Global Optimization 25, 23–42 (2003). https://doi.org/10.1023/A:1021386030224
Issue Date:
DOI: https://doi.org/10.1023/A:1021386030224