Entropy as a quality descriptor for the dose distribution — theory and practice for the patient target volume

The most common and established way to evaluate the quality of a radiotherapy plan is to use the dose-volume histogram (DVH). The evaluation of the DVH, however, is a subjective procedure. This may not be crucial as long as the two plans are significantly different. In the case of several plans obtained with different planning or optimisation strategies the differences are often subtle and therefore a more objective comparison method is desirable. A commonly used approach is based on evaluation of the conformity index, however we show how it can fail for plans of similar quality.

Therefore we propose a new method based on the similarity of DVH to statistical distributions, which can be characterised uniquely by their entropy. The concept is defined separately for target volumes, where it is derived from the Fermi-like distribution, and for organs at risk, where the traditional approach is also considered in its derivation. The artificial illustratory and clinical examples show the properties of the entropy as the quality descriptor and compare it to the conformity index. The examples are focused to the patient target volumes, where the advantage of the concept is more evident.