An inverse problem in radiation therapy

The mathematical formalism associated with a 2-dimensional inverse problem in radiation therapy treatment and planning is discussed. The formalism is extended to convex phantoms of arbitrary cross-section. Relations necessary to produce circularly symmetric dose distributions about any point within the phantom are obtained. The general case for a particularly simple class of ideal dose distributions within 2-dimensional convex phantoms of arbitrary shape is solved. The relationship between treatment beans with and without negative fluences, and their associated dose distributions, is discussed.