Material elemental decomposition in dual and multi‐energy CT via a sparsity‐dictionary approach for proton stopping power ratio calculation - Shen, Chenyang; Li, Bin; Chen, Liyuan; Yang, Ming; Lou, Yifei; Jia, Xun (Medical physics (Lancaster), 2018)
Purpose Accurate calculation of proton stopping power ratio (SPR) relative to water is crucial to proton therapy treatment planning, since SPR affects prediction of beam range. Current standard practice derives SPR using a single CT scan. Recent studies showed that dual‐energy CT (DECT) offers advantages to accurately determine SPR. One method to further improve accuracy is to incorporate prior knowledge on human tissue composition through a dictionary approach. In addition, it is also suggested that using CT images with multiple (more than two) energy channels, i.e., multi‐energy CT (MECT), can further improve accuracy. In this paper, we proposed a sparse dictionary‐based method to convert CT numbers of DECT or MECT to elemental composition (EC) and relative electron density (rED) for SPR computation. Method A dictionary was constructed to include materials generated based on human tissues of known compositions. For a voxel with CT numbers of different energy channels, its EC and rED are determined subject to a constraint that the resulting EC is a linear non‐negative combination of only a few tissues in the dictionary. We formulated this as a non‐convex optimization problem. A novel algorithm was designed to solve the problem. The proposed method has a unified structure to handle both DECT and MECT with different number of channels. We tested our method in both simulation and experimental studies. Results Average errors of SPR in experimental studies were 0.70% in DECT, 0.53% in MECT with three energy channels, and 0.45% in MECT with four channels. We also studied the impact of parameter values and established appropriate parameter values for our method. Conclusion The proposed method can accurately calculate SPR using DECT and MECT. The results suggest that using more energy channels may improve the SPR estimation accuracy.