H. Edwin Romeijn, James F. Dempsey, Jonathan G. Li
A unifying framework for multi-criteria fluence map optimization models
Models for finding treatment plans for intensity modulated
radiation therapy are usually based on a number of structure-based
treatment plan evaluation criteria, which are often conflicting.
Rather than formulating a model that a priori quantifies
the trade-offs between these criteria, we consider a
multi-criteria optimization approach that aims at finding those
so-called undominated treatment plans for which a real
trade-off is necessary. We present a unifying framework for
studying multi-criteria optimization problems for treatment
planning that establishes conditions under which treatment plan
evaluation criteria can be transformed into convex criteria while
preserving the set of undominated treatment plans. Such
transformations are identified for many of the criteria that have
been proposed to date. This establishes equivalences between many
of the criteria which have previously been thought to be unique.
Additionally, it is shown that use of a nonconvex criterion can
often be avoided by transformation to an equivalent convex
criterion. In particular, we show that models employing criteria
such as tumor control probability, normal tissue complication
probability, probability of uncomplicated tumor control, as well
as sigmoidal transformations of (generalized) equivalent uniform
dose are equivalent to models formulated in terms of (generalized)
equivalent uniform dose criteria only. In addition, we show that
equivalent models using voxel-based criteria that penalize dose in
individual voxels exist as well.