A Bayesian approach to solve proton stopping powers from noisy multi‐energy CT data

Purpose To propose a new formalism allowing the characterization of human tissues from multienergy computed tomography (MECT) data affected by noise and to evaluate its performance in estimating proton stopping powers (SPR). Methods A recently published formalism based on principal component analysis called eigentissue decomposition (ETD) is adapted to the context of noise using a Bayesian estimator. The method, named Bayesian ETD, uses the maximum a posteriori fractions of eigentissues in each voxel to determine physical parameters relevant for proton beam dose calculation. Simulated dual‐energy computed tomography (DECT) data are used to evaluate the performance of the proposed method to estimate SPR and to compare it to the initially proposed maximum‐likelihood ETD and to a state‐of‐the‐art ρe − Z formalism. To test the robustness of each method towards clinical reality, three different levels of noise are implemented, as well as variations in elemental composition and density of reference tissues. The impact of using more than two energy bins to determine SPR is also investigated by simulating MECT data using two to five energy bins. Finally, the impact of using MECT over DECT for range prediction is evaluated using a probabilistic model. Results For simulated DECT data of reference tissues, the Bayesian ETD approach systematically gives lower root‐mean‐square (RMS) errors with negligible bias. For a medium level of noise, the RMS errors on SPR are found to be 2.78%, 2.76% and 1.53% for ρe − Z, maximum‐likelihood ETD, and Bayesian ETD, respectively. When variations are introduced to the elemental composition and density, all implemented methods give similar performances at low noise. However, for a medium noise level, the proposed Bayesian method outperforms the two others with a RMS error of 1.94%, compared to 2.79% and 2.78% for ρe − Z and maximum‐likelihood ETD, respectively. When more than two energy spectra are used, the Bayesian ETD is able to reduce RMS error on SPR using up to five energy bins. In terms of range prediction, Bayesian ETD with four energy bins in realistic conditions reduces proton beam range uncertainties by a factor of up to 1.5 compared to ρe − Z. Conclusion The Bayesian ETD is shown to be more robust against noise than similar methods and a promising approach to extract SPR from noisy DECT data. In the advent of commercially available multi‐energy CT or photon‐counting CT scanners, the Bayesian ETD is expected to allow extracting more information and improve the precision of proton therapy beyond DECT.

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