Fuzzy modeling and optimization of planning in radiotherapy

Radiation therapy concerns the delivery of a proper dose of radiation to a tumor volume without causing irreparable damage to, surrounding healthy tissues and critical organs. Radiotherapy planning involves a forward problem and an inverse problem. The forward problem is to calculate the dose distribution within a given volume due to a specific configuration of radiation sources. The inverse problem calls for the identification of a physical configuration which when is actually applied to a given volume, will result in a prescribed dose distribution. The problem of plan combination, formulated and studied here, is neither of forward nor of inverse type. It addresses a situation where for a specific clinical case, a set of several treatment plans is presented for all of which both the forward and the inverse problem have already been solved using whatever available methods. Here, the authors represent treatment plans as vectors in Euclidean space and define their acceptability and realizability. A model for achieving a new combined treatment plan is given, and with appropriate constraints, the combined treatment plan is forced to be acceptable. Two criteria to optimize the planning procedure are introduced and formulated using plan combination concept. In summary, a new approach, based on fuzzy set theory, for modeling and optimization of plan combination in radiotherapy is proposed. Precise mathematical definitions are introduced and two reasonable objective functions for planning procedure is formulated. Based on fuzzy mathematical programming, the problems are solved and the results are compared. Numerical examples illustrate the proposed idea and the features and performance of the above methodology is discussed.