Systematic analysis of the impact of imaging noise on dual-energy CT-based proton stopping power ratio estimation

Purpose: Dual-energy CT (DECT) has been shown to have a great potential in reducing the uncertainty in proton stopping power ratio (SPR) estimation, when compared to current standard method — the stoichiometric method based on single-energy CT (SECT). However, a few recent studies indicated that imaging noise may have a substantial impact on the performance of the DECT-based approach, especially at a high noise level. The goal of this study is to quantify the uncertainty in SPR and range estimation caused by noise in the DECT-based approach under various conditions. Methods: Two widely referred parametric DECT methods were studied: the Hünemohr-Saito (HS) method and the Bourque method. Both methods were calibrated using Gammex tissue substitute inserts scanned on the Siemens Force DECT scanner. An energy pair of 80 and 150 kVp with a tin filter was chosen to maximize the spectral separation. After calibrating the model with the Gammex phantom, CT numbers were synthesized using the density and elemental composition from ICRU 44 human tissues to be used as a reference, in order to evaluate the impact of noise alone while putting aside other sources of uncertainty. Gaussian noise was introduced to the reference CT numbers and its impact was measured with the difference between estimated SPR and its noiseless reference SPR. The uncertainty caused by noise was divided into two independent categories: shift of the mean SPR and variation of SPR. Their overall impact on range uncertainty was evaluated on homogeneous and heterogeneous tissue samples of various water equivalent path lengths (WEPL). Results: Due to the algorithms being nonlinear and/or having hard thresholds in the CT number to SPR mapping, noise in the CT numbers induced a shift in the mean SPR from its noiseless reference SPR. The degree of the mean shift was dependent on the algorithm and tissue type, but its impact on the SPR uncertainty was mostly small compared to the variation. All mean shifts observed in this study were within 0.5% at a noise level of 2%. The ratio of the influence of variation to mean shift was mostly greater than 1, indicating that variation more likely determined the uncertainty caused by noise. Overall, the range uncertainty (95th percentile) caused by noise was within 1.2% and 1.0% for soft and bone tissues, respectively, at 2% noise with 50 voxels. This value can be considered an upper limit as more voxels and lower noise level rapidly decreased the uncertainty. Conclusions: We have systematically evaluated the impact of noise to the DECT-based SPR estimation and identified under various conditions that the variation caused by noise is the dominant uncertainty-contributing component. We conclude that, based on the noise level and tumor depth, it is important to estimate and include the uncertainty due to noise in estimating the overall range uncertainty before implementing a small margin in the range of 1%.