Robust treatment planning for brachytherapy using mixed integer linear programming



Radiation therapy is a common treatment for cancer, where ionizing radiation is administered in order to eradicate tumor cells. When administering radiation to the tumor, the surrounding healthy tissues inevitably receive radiation as well. Treatment planning for radiation therapy aims at finding a treatment plan (i.e., it chooses radiation source locations, radiation times and intensities, etc.) such that the tumor receives a therapeutic dose, while the inevitable dose delivery to the surrounding healthy organs remains limited. Mathematical optimization techniques are used to find the optimal treatment plan and dose distribution for each individual patient based on medical images showing the patient's anatomy, tumor and surrounding organs. Various optimization approaches have been described in the literature and some have been implemented in commercially available treatment planning systems.

In this talk I will discuss robust treatment planning for brachytherapy for prostate cancer. Brachytherapy is a type of radiation therapy where radiation is delivered from within the tumor. A treatment plan where the tumor dose is maximized while satisfying restrictions on the dose to the healthy organs can be found using a mixed integer linear program. However, the input to this model is uncertain: it is difficult to observe the exact size, shape and position of the tumor and healthy organs. This results in a risk of an overdose to the healthy organs or an undesirably low dose to the tumor. From a mathematical point of view the uncertainty in organ locations results in uncertainty in index sets. We propose a method that extends robust optimization, that is developed to account for uncertainty in model parameters, to account for uncertainties in index sets. The robust treatment planning model finds a treatment plan that is robust against uncertainties in organ positions and mitigates the risks of underdosing the tumor and overdosing the healthy organs.

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