# Decomposition analysis of differential dose volume histograms

*Medical Physics*. 2006 Feb;33(2):297-307. [Link]

Van den Heuvela F.

Department of Oncology and Experimental Radiation Therapy, Universiteit Leuven, Belgium. frank.vandenheuvel@uz.kuleuven.ac.be

### Abstract

Dose volume histograms are a common tool to assess the value of a treatment plan for various forms of radiation therapy treatment. The purpose of this work is to introduce, validate, and apply a set of tools to analyze differential dose volume histograms by decomposing them into physically and clinically meaningful normal distributions. A weighted sum of the decomposed normal distributions (e.g., weighted dose) is proposed as a new measure of target dose, rather than the more unstable point dose. The method and its theory are presented and validated using simulated distributions. Additional validation is performed by analyzing simple four field box techniques encompassing a predefined target, using different treatment energies inside a water phantom. Furthermore, two clinical situations are analyzed using this methodology to illustrate practical usefulness. A comparison of a treatment plan for a breast patient using a tangential field setup with wedges is compared to a comparable geometry using dose compensators. Finally, a normal tissue complication probability (NTCP) calculation is refined using this decomposition. The NTCP calculation is performed on a liver as organ at risk in a treatment of a mesothelioma patient with involvement of the right lung. The comparison of the wedged breast treatment versus the compensator technique yields comparable classical dose parameters (e.g., conformity index approximately = 1 and equal dose at the ICRU dose point). The methodology proposed here shows a 4% difference in weighted dose outlining the difference in treatment using a single parameter instead of at least two in a classical analysis (e.g., mean dose, and maximal dose, or total dose variance). NTCP-calculations for the mesothelioma case are generated automatically and show a 3% decrease with respect to the classical calculation. The decrease is slightly dependant on the fractionation and on the alpha/beta-value utilized. In conclusion, this method is able to distinguish clinically important differences between treatment plans using a single parameter. This methodology shows promise as an objective tool for analyzing NTCP and doses in larger studies, as the only information needed is the dose volume histogram.