Are gamma passing rate and dose-volume histogram QA metrics correlated?

Abstract

Purpose: The quality of a measured distribution of dose delivered against its corresponding radiotherapy plan is routinely assessed by gamma index (GI) and dose-volume histogram (DVH) metrics. Any correlation between error detection rates, as based on either of these approaches, while argued, has never been convincingly demonstrated. The dependence of the strength of correlation between the GI passing rate ( $\gamma P$ ) and DVH quality assurance (QA) metrics on various elements of the therapy plan has not been systematically investigated.

Methods: A formal analysis of the relation between $\gamma P$ and DVH metrics has been undertaken, leading to a relationship which may partly approximate $\gamma P$ with respect to the DVH. This relationship was further validated by studying examples of simulated clinical radiotherapy plans and by studying the correlation between $\gamma P$ and the derived relationship using a simple two-dimensional representations of the planning target volume (PTV) and organs at risk (OAR), where penumbra regions, distance-to-agreement tolerances and dose delivery errors were systematically varied.

Results: It is shown formally that there cannot be any correlation between $\gamma P$ and other commonly applied DVH-derived QA measures. However, $\gamma P$ may be partly approximated given the planned and measured DVH. The derived $\gamma P$ approximation (the " $\gamma$ -slope indicator") may be clinically useful in some practical cases of radiotherapy plan QA.

Conclusions: In formal terms, there cannot be any correlation between $\gamma P$ and any common DVH-calculated patient-specific measures, with respect to PTV or OAR. However, as demonstrated analytically and further confirmed in our simulation studies, the $\gamma P$ approximation derived in this study (the " $\gamma$ -slope indicator") may in some cases offer a degree of correlation between $\gamma P$ and the PTV and OAR DVH QA metrics in measured and planned patient-specific dose distributions-which may be potentially useful in clinical practice.

Keywords: correlation analysis; dose volume histogram; gamma index; radiotherapy.