A Novel Nonlinear Multi-Material Decomposition Framework Using Harmonic Coordinates for Improved Quantitative Dual-Energy CT
Abstract
Purpose
Conventional Dual-Energy CT (DECT) multi-material decomposition (MMD) often suffers from systematic bias due to linear mixing assumptions that fail to account for nonlinear attenuation effects like beam hardening and scatter. These instabilities are magnified in large patients or low-dose protocols. We developed and validated a nonlinear harmonic-coordinate MMD (HC-MMD) framework designed to improve the quantitative accuracy of iodine and calcium separation by directly modeling curved attenuation manifolds.
Methods
A thoracic phantom with iodine (2–20 mg/mL) and hydroxyapatite (50–400 mg/mL) inserts was scanned on a clinical photon-counting CT (PCCT) system. Robustness was evaluated across multiple phantom sizes (small to large) and dose levels spanning 6 to 55 mGy. HC-MMD precomputes coordinate fields by solving Laplace’s equation on a finite-element mesh, performing voxel-wise decomposition via harmonic interpolation. Accuracy was compared against prior methods using independent validation rods. A clinical proof-of-concept (n=5) compared virtual non-contrast (VNC) images against true non-contrast (TNC) references.
Results
HC-MMD significantly outperformed previous methods. Average iodine RMSE was reduced by 82% across phantom sizes (0.06–0.25 mg/mL) and 80% across dose levels (0.10–0.41 mg/mL). Calcium RMSE decreased by 87% (3.59–5.20 mg/mL) and 86% (2.97–9.37 mg/mL), respectively. While linear techniques showed substantial residuals (up to 87%), HC-MMD maintained residuals below 1.2%. In clinical cases, HC-MMD reduced VNC RMSE by approximately 30% compared to vendor-specific and conventional algorithms, effectively suppressing non-physical artifacts.
Conclusion
HC-MMD effectively overcomes the limitations of linear decomposition by explicitly modeling nonlinear attenuation behavior. The framework provides superior iodine and calcium quantification and maintains high stability even in low-dose PCCT settings. This approach offers a robust path for improving the reliability of quantitative spectral imaging in diverse clinical populations.