Configuration options for intensity-modulated radiation therapy using multiple static fields shaped by a multileaf collimator

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Abstract
One-dimensional (1D) intensity-modulated beams (IMBs) can be generated by multiple static fields (MSFs) created by a multileaf collimator (MLC) with the radiation switched off between field re-settings (Bortfeld-Boyer method). Each component irradiation is of equal fluence. This paper presents and analyses the formulae for the number of physically allowed combinations of leaf settings which generate any given IMB. The formulae are general to an IMB with any number of local minima and extend from the well-known formula for a single-peaked IMB with N left-leaf (L-leaf) and N right-leaf (R-leaf) positions. A `combination' is a set of N L-leaf and R-leaf pairings. A `physically allowed combination' is one in which no L-leaf is paired with an R-leaf to its left. The physically allowed combinations are grouped by specific properties into classes in which the well-known techniques of `leaf-sweep' and `close-in' are just two members. Consideration of these properties leads to a new suggestion of the `forced-baseline' configuration in which the first intensity increment is delivered for the full field width and there remain choices concerning the delivery of the rest of the IMB within which two different possibilities are `one-out-of-sync leaf-sweep' and `minimum leaf travel'. The extension to 2D is briefly introduced.