The effect of set-up uncertainties, contour changes, and tissue inhomogeneities on target dose-volume histograms

Understanding set-up uncertainty effects on dose distributions is an important clinical problem but difficult to model accurately due to their dependence on tissue inhomogeneities and changes in the surface contour (i.e., variant effects). The aims are: (1) to evaluate and quantify the invariant and variant effects of set-up uncertainties, contour changes and tissue inhomogeneities on target dose-volume histograms (DVHs); (2) to propose a method to interpolate (variant) DVHs. We present a lung cancer patient to estimate the significance of set-up uncertainties, contour changes and tissue inhomogeneities in target DVHs. Differential DVHs are calculated for 15 displacement errors (with respect to the isocenter) using (1) an invariant shift of the dose distribution at the isocenter, (2) a full variant calculation, and (3) a B-spline interpolation applied to sparsely sampled variant DVHs. The collapsed cone algorithm was used for all dose calculations. Dosimetric differences are quantified with the root mean square (RMS) deviation and the equivalent uniform dose (EUD). To determine set-up uncertainty effects, weighted mean EUDs, assuming normally distributed displacement errors, are used. The maximum absolute difference and RMS deviation in the integral DVHs' relative dose between (1) the invariant and calculated curves are 65.2% and 5.8% and (2) the interpolated and calculated curves are 16.9% and 2.5%. Similarly, the maximum absolute difference and RMS deviation in mean EUD as a function of the set-up uncertainty's standard deviation between (1) the invariant and calculated curves are 0.02 and 0.01 Gy; and (2) the interpolated and calculated curves are 0.01 and 0.006 Gy. Since a "worst-case" example is selected, we conclude that, in the majority of clinical cases, the variant effects of contour changes, tissue inhomogeneities and set-up uncertainties on EUD are negligible. Interpolation is a valid, efficient method to approximate DVHs.