Optimal Field Splitting, with Applications in Intensity-Modulated Radiation Therapy

摘要

We consider an interesting geometric partition problem called field splitting, which arises in intensity-modulated radiation therapy (IMRT). IMRT is a modern cancer treatment technique that delivers prescribed radiation dose distributions, called intensity maps (IMs) and defined on uniform grids, to target tumors via the help of a device called the multileaf collimator (MLC). The delivery of each IM requires a certain amount of beam-on time, which is the total time when a patient is exposed to actual irradiation during the delivery. Due to the maximum leaf spread constraint of the MLCs (i.e., the size and range of an MLC are constrained by its mechanical design), IMs whose widths exceed a given threshold value cannot be delivered by the MLC as a whole, and thus must be split into multiple subfields (i.e., subgrids) so that each sub-field can be delivered separately by the MLC. In this paper, we present the first efficient algorithm for computing an optimal field splitting that guarantees to minimize the total beam-on time of the resulting subfields subject to a new constraint that the maximum beam-on time of each individual subfield is no larger than a given a threshold value. Our basic idea is to formulate this field splitting problem as a special integer linear programming problem. By considering its dual problem, which turns out to be a shortest path problem on a directed graph with both positive and negative edge weights, we are able to handle efficiently the upper-bound constraint on the allowed beam-on time of each resulting individual subfield. We implement our new field splitting algorithm and give some experimental results on comparing our solutions with those computed by the previous methods.