Investigations of Computational Optimization in Brachytherapy Cancer Treatment
This project brings together researchers in computational optimization and medicine to address the fundamental problem of treatment planning for brachytherapy treatment of cancer. The project involves four avenues of investigation: 1) Design of realistic and practical mathematical models based on mixed integer programming (MIP) technology to describe the physical planning of brachytherapy, which involves the determination of an ``optimal'' configuration of radioactive sources to be implanted in/near the tumor. 2) Theoretical investigation of the underlying polyhedral structure of the MIP models via the construction of conflict hypergraphs. Associated polyhedral implications will be exploited to develop and implement separation algorithms to assist in the solution process. 3) Develop new computational tools aimed at solving the difficult dense MIP instances from this class of problems, as well as from other applications. Computational approaches include matrix reduction techniques, penalty branching strategies, aggregate branching which focuses on reduced-cost and multiple branches with sets of variables instead of variable dichotomy, and generation of strong cutting planes from hypergraphic structures. 4) Integration of the mathematical models and computational engine into an expert planning system for use in the operating room.
The success of the research will lead to important theoretical results related to integer programming through the hypergrahic constructs; it will lead to computational advances for solving dense MIP instances, a characteristic rather different from most industrial applications, but arising commonly in medical diagnosis and treatment planning problems; and it will improve the ability to treat patients in the best possible way. Furthermore, the resulting treatment planning system will serve as a research tool to push the frontier of understanding for brachytherapy treatment, opening up the possibility of conducting clinical investigations which require unbiased plans to be produced within a short time frame.
Educational outreach involves developing teaching materials related to the project for undergraduate and graduate students in engineering and in the medical domain. It also involves training of 2 Ph.D. students in this multidisciplinary research involving optimization, algorithmic design and cancer treatment. The Ph.D. research will focus on theoretical and computational optimization, and in particular, on issues related to the project herein. Undergraduates and minorities will be involved in the research experience through undergraduate courses and regular premed and minority student mentoring. Part of the research project will also be disseminated in the lectures on information and biotechnology in the course ``Cancer Biology and Biotechnology'', developed recently by a group of interdisciplinary faculty researchers at Georgia Tech with a focus on multi-faceted approaches for advancing cancer technology. Mention of this new educational effort highlighting applications of engineering technology in medical/oncological research will be included in possible panel discussions and in the recruitment of high school students.
