Dose reconstruction in deforming lung anatomy: dose grid size effects and clinical implications

In this study we investigated the accumulation of dose to a deforming anatomy (such as lung) based on voxel tracking and by using time weighting factors derived from a breathing probability distribution function (p.d.f.). A mutual information registration scheme (using thin-plate spline warping) provided a transformation that allows the tracking of points between exhale and inhale treatment planning datasets (and/or intermediate state scans). The dose distributions were computed at the same resolution on each dataset using the Dose Planning Method (DPM) Monte Carlo code. Two accumulation/interpolation approaches were assessed. The first maps exhale dose grid points onto the inhale scan, estimates the doses at the "tracked" locations by trilinear interpolation and scores the accumulated doses (via the p.d.f.) on the original exhale data set. In the second approach, the "volume" associated with each exhale dose grid point (exhale dose voxel) is first subdivided into octants, the center of each octant is mapped to locations on the inhale dose grid and doses are estimated by trilinear interpolation. The octant doses are then averaged to form the inhale voxel dose and scored at the original exhale dose grid point location. Differences between the interpolation schemes are voxel size and tissue density dependent, but in general appear primarily only in regions with steep dose gradients (e.g., penumbra). Their magnitude (small regions of few percent differences) is less than the alterations in dose due to positional and shape changes from breathing in the first place. Thus, for sufficiently small dose grid point spacing, and relative to organ motion and deformation, differences due solely to the interpolation are unlikely to result in clinically significant differences to volume-based evaluation metrics such as mean lung dose (MLD) and tumor equivalent uniform dose (gEUD). The overall effects of deformation vary among patients. They depend on the tumor location, field size, volume expansion, tissue heterogeneity, and direction of tumor displacement with respect to the beam, and are more likely to have an impact on serial organs (such as esophagus), rather than on large parallel organs (such as lung).