Model-based three-material decomposition in dual-energy CT using the volume conservation constraint

Objective. We develop a model-based optimization algorithm for 'one-step' dual-energy (DE) CT decomposition of three materials directly from projection measurements.Approach.Since the three-material problem is inherently undetermined, we incorporate the volume conservation principle (VCP) as a pair of equality and nonnegativity constraints into the objective function of the recently reported model-based material decomposition (MBMD). An optimization algorithm (constrained MBMD, CMBMD) is derived that utilizes voxel-wise separability to partition the volume into a VCP-constrained region solved using interior-point iterations, and an unconstrained region (air surrounding the object, where VCP is violated) solved with conventional two-material MBMD. Constrained MBMD (CMBMD) is validated in simulations and experiments in application to bone composition measurements in the presence of metal hardware using DE cone-beam CT (CBCT). A kV-switching protocol with non-coinciding low- and high-energy (LE and HE) projections was assumed. CMBMD with decomposed base materials of cortical bone, fat, and metal (titanium, Ti) is compared to MBMD with (i) fat-bone and (ii) fat-Ti bases.Main results.Three-material CMBMD exhibits a substantial reduction in metal artifacts relative to the two-material MBMD implementations. The accuracies of cortical bone volume fraction estimates are markedly improved using CMBMD, with ∼5-10× lower normalized root mean squared error in simulations with anthropomorphic knee phantoms (depending on the complexity of the metal component) and ∼2-2.5× lower in an experimental test-bench study.Significance.In conclusion, we demonstrated one-step three-material decomposition of DE CT using volume conservation as an optimization constraint. The proposed method might be applicable to DE applications such as bone marrow edema imaging (fat-bone-water decomposition) or multi-contrast imaging, especially on CT/CBCT systems that do not provide coinciding LE and HE ray paths required for conventional projection-domain DE decomposition.