Non-unique water and contrast agent solutions in dual-energy CT

Abstract

The goal of this work is to study occurrences of non-unique solutions in dual-energy CT (DECT) for objects containing water and a contrast agent. Previous studies of the Jacobian of nonlinear systems identified that a vanishing Jacobian determinant indicates the existence of multiple solutions to the system. Vanishing Jacobian determinants are identified for DECT setups by simulating intensity data for practical thickness ranges of water and contrast agent. Once existence is identified, non-unique solutions are found by simulating scan data and finding intensity contours with that intersect multiple times. With this process non-unique solutions are found for DECT setups scanning iodine and gadolinium, including setups using tube potentials in practical ranges. Non-unique solutions demonstrate a large range of differences and can result in significant discrepancies between recovered and true material mapping.

Keywords: Dual-energy CT image reconstruction; contrast agents; non-uniqueness.

Fig. 1.

Plots of Jacobian determinant for thickness sweep. The blue and red curves correspond to the maximum and minimum values of the determinant among all thickness combinations. High tube potential was held at 120 kVp and low tube potential was varied from 30 to 100 kVp. Materials were water and iodine (left) or gadolinium (right).

Fig. 2.

Intensity sweep plots for water and iodine. Low tube potential increases from 30 kVp to 50 kVp moving left to right and high tube potential increases from 70 kVp to 140 kVp moving top to bottom. Black areas indicate intensity combinations that only have one solution to Eq. 1 and red areas indicate where there are two solutions.

Fig. 3.

Intensity sweep plots for water and gadolinium. Low tube potential increases from 40 kVp to 80 kVp moving left to right and high tube potential increases from 100 kVp to 140 kVp moving top to bottom. Black areas indicate intensity combinations that only have one solution to Eq. 1 and red areas indicate where there are two solutions.

Fig. 4.

Selected solution plots for water and iodine. Low tube potential is held at 50 kVp and high tube potential increases from 70 to 100 kVp from left to right. The same solution plots from Fig. 2 are shown (top) along with corresponding histograms of the Euclidean distance between each pair of solutions for a given intensity pair (bottom).

Fig. 5.

Selected solution plots for water and gadolinium. Low tube potential is held at 40 kVp and high tube potential increases from 100 to 140 kVp from left to right. The same solution plots from Fig. 3 are shown (top) along with corresponding histograms of the Euclidean distance between each pair of solutions for a given intensity pair (bottom).