Electron density and effective atomic number estimation in a maximum a posteriori framework for dual‐energy computed tomography
Authors: Simard Mikaël , Bär Esther , Blais Danis , Bouchard Hugo 
Published: June 2020

PurposeThe stoichiometric calibration method for dual‐energy CT (DECT) proposed by Bourque et al. (Phys Med Biol. 59:2059; 2014), which provides estimators of the electron density and the effective atomic number, is adapted to a maximum a posteriori (MAP) framework to increase the model’s robustness to noise and biases in CT data, specifically for human tissues. Robust physical parameter estimation from noisy DECT scans is required to maximize the precision of quantities used for radiotherapy treatment planning such as the proton stopping power (SPR).MethodsEstimation of electron density and effective atomic number is performed by constraining their variation to the natural range of values expected for human tissues, while maximizing attenuation data fidelity. The MAP framework is first compared against the original method using theoretical CT numbers with Gaussian noise. The quantitative accuracy of the MAP framework is then validated experimentally on the Gammex 467 phantom. Then, using two clinical datasets, the advantages of the approach are experimentally evaluated, qualitatively, and quantitatively.ResultsThe theoretical study shows that the root‐mean‐square error on the electron density, the effective atomic number and the SPR are, respectively, reduced from 2.3 to 1.5, 5.7 to 3.2 and 2.8 to 1.7% with the adapted framework, when analyzing soft tissues and bone together. The experimental validation study shows that the standard deviation in Gammex inserts can be reduced, on average, by factors of 1.4 (electron density), 2.7 (effective atomic number), and 1.9 (SPR), while the quantitative accuracy of the three physical parameters is preserved, on average. Evaluation on clinical datasets show apparent noise reduction in maps of all estimated physical quantities, and suggests that the MAP framework has increased robustness to beam hardening and photon starvation artifacts. Mean values for the electron density, the effective atomic number, and the SPR averaged in four uniform regions of interest (brain, muscle, adipose, and cranium), respectively, differ by 0.7, 1.8, and 0.9% between both frameworks. The standard deviation in the same regions of interest is also reduced, on average, by factors of 1.8, 6.6, and 3.2 with the MAP framework. Differences in mean value and standard deviations are statistically significant.ConclusionTheoretical and experimental results suggest that the MAP framework produces more accurate and precise estimates of the electron density and SPR. Thus, the present approach limits the propagation of noise in DECT attenuation data to radiotherapy‐related parameters maps such as the SPR and the electron density. Using a MAP framework with DECT for radiotherapy treatment planning can help maximizing the precision of dose calculation. The method also provides more precise estimates of the effective atomic number. The MAP methodology is presented in a general way such that it can be adapted to any DECT image‐based tissue characterization method.