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A coupled column generation, mixed integer approach to optimal planning of intensity modulated radiation therapy for cancer

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Abstract.

Approximately 40% of all U.S. cancer cases are treated with radiation therapy. In Intensity-Modulated Radiation Therapy (IMRT) the treatment planning problem is to choose external beam angles and their corresponding intensity maps (showing how the intensity varies across a given beam) to maximize tumor dose subject to the tolerances of surrounding healthy tissues. Dose, like temperature, is a quantity defined at each point in the body, and the distribution of dose is determined by the choice of treatment parameters available to the planner. In addition to absolute dose limits in healthy tissues, some tissues have at least one dose-volume restriction that requires a fraction of its volume to not exceed a specified tighter threshold level for damage. There may also be a homogeneity limit for the tumor that restricts the allowed spread of dose across its volume. We formulate this planning problem as a mixed integer program over a coupled pair of column generation processes -- one designed to produce intensity maps, and a second specifying protected area choices for tissues under dose-volume restrictions. The combined procedure is shown to strike a balance between computing an approximately optimal solution and bounding its maximum possible suboptimality that we believe holds promise for implementations able to offer the power and flexibility of mixed-integer linear programming models on instances of practical scale.

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Authors and Affiliations

  1. Industrial Engineering, Purdue, University

    Felisa Preciado-Walters & Ronald Rardin

  2. Indiana, University, School of Medicine

    Mark Langer & Van Thai

Authors
  1. Felisa Preciado-Walters
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  2. Ronald Rardin
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  3. Mark Langer
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  4. Van Thai
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Additional information

A portion of the work of Dr. Langer, Mr. Thai and Dr. Preciado-Walters was supported by National Science Foundation grant ECS-0120145 and National Cancer Institute 1R41CA91688-01. Dr. Rardin is participated while on rotation as Program Director for Operations Research and Service Enterprise Engineering at the National Science Foundation.

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Preciado-Walters, F., Rardin, R., Langer, M. et al. A coupled column generation, mixed integer approach to optimal planning of intensity modulated radiation therapy for cancer. Math. Program., Ser. A 101, 319–338 (2004). https://doi.org/10.1007/s10107-004-0527-6

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  • DOI: https://doi.org/10.1007/s10107-004-0527-6

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