The delta index: a novel metric to assess dose accumulation uncertainty in MR-guided radiotherapy

Abstract

Purpose or Objective Accumulating actually delivered dose in MR-guided radiotherapy remains challenging due to the short-comings of Deformable Image Registration (DIR). The uncertainties associated with cumulative MR-linac dose distributions were estimated by postulating a new metric, the delta (δ) index. Materials and Methods Image registration and cumulative dose distributions for five lung SBRT patients treated on the MR-linac were calculated using Advanced Medical Image Registration Engine (ADMIRE, Elekta AB). The unitless δ index was calculated for each voxel of the accumulated dose distribution by simultaneously assessing dose and spatial differences to all neighbouring voxels (Eq. 1). To estimate the spatial uncertainty of the DIR, the distance discordance metric (DDM) was calculated, where voxels were traced between two reference fractions via the remaining fractions. The DDM acts as a characteristic length in a Gaussian distribution that defines the near and far neighbourhood of each reference voxel. It was assumed that the neighbouring voxel with the largest distance-weighted dose deviation might represent the true dose value for the reference voxel. The δ index was thus taken as the maximum value calculated over all evaluated voxels (Eq. 2). In analogy to the widely-used Gamma index, the δ index passing rate is the percentage of points satisfying the passing criteria (Eq. 3). The dependence of the δ index passing rate on the parameters used for each calculation were investigated using different dose tolerance criteria and DDM distributions, for threshold doses of at least 20% and 90% of the Prescription Dose (PD). The δ index script is available at: https://github.com/DeltaIndex/CodeDeltaIndex. Results The δ index passing rate showed that the voxels that failed to meet the criteria were predominantly in the low dose regions (Fig. 2). Using a 3% local dose tolerance, the δ index passing rate in the body contour ranged between 59-88% (PD 20%) and 64-98% (PD 90%). The mean ± SD of the δ index ranged from 0.41 ± 0.68 to 1.48 ± 2.35 (PD 20%) and from 0.17 ± 0.29 to 0.88 ± 0.73 (PD 90%), for all patients. The δ index passing rate decreased in all patients when using 2% instead of 3% local dose tolerance, ranging between 48-84% (PD 20%) and 49-94% (PD 90%). The δ ndex passing rates were near identical using different reference fractions to calculate the DDM, and ranged between 57-89% (PD 20%) and 60-99% (PD 90%). Conclusion The novel δ index quantifies the uncertainty of accumulated dose distributions in MR-guided radiotherapy. For MR-guided lung SBRT, the δ index passing rate increased in the high dose region indicating more reliably accumulated doses. The relatively low dependency of the δ index passing rate on different dose tolerance criteria and DDM distributions show the robustness of this metric to its parameterisation.