Estimation of three‐dimensional intrinsic dosimetric uncertainties resulting from using deformable image registration for dose mapping

Abstract

This article presents a general procedural framework to assess the point-by-point precision in mapped dose associated with the intrinsic uncertainty of a deformable image registration (DIR) for any arbitrary patient. Dose uncertainty is obtained via a three-step process. In the first step, for each voxel in an imaging pair, a cluster of points is obtained by an iterative DIR procedure. In the second step, the dispersion of the points due to the imprecision of the DIR method is used to compute the spatial uncertainty. Two different ways to quantify the spatial uncertainty are presented in this work. Method A consists of a one-dimensional analysis of the modules of the position vectors, whereas method B performs a more detailed 3D analysis of the coordinates of the points. In the third step, the resulting spatial uncertainty estimates are used in combination with the mapped dose distribution to compute the point-by-point dose standard deviation. The process is demonstrated to estimate the dose uncertainty induced by mapping a 62.6 Gy dose delivered on maximum exhale to maximum inhale of a ten-phase four-dimensional lung CT. For the demonstration lung image pair, the standard deviation of inconsistency vectors is found to be up to 9.2 mm with a mean sigma of 1.3 mm. This uncertainty results in a maximum estimated dose uncertainty of 29.65 Gy if method A is used and 21.81 Gy for method B. The calculated volume with dose uncertainty above 10.00 Gy is 602 cm3 for method A and 1422 cm3 for method B. This procedure represents a useful tool to evaluate the precision of a mapped dose distribution due to the intrinsic DIR uncertainty in a patient. The procedure is flexible, allowing incorporation of alternative intrinsic error models.