Mitigating Boundary Artifacts In 5T MRI Electrical Properties Tomography Via Condition-Number-Guided Adaptive Differentiation and Spatially Varying PDE Constraints
Abstract
Purpose
To address severe boundary artifacts in Electrical Properties Tomography (EPT) reconstruction caused by noise amplification and erroneous numerical differentiation across tissue discontinuities. A unified, boundary-aware reconstruction framework is proposed, which is applicable to both Laplacian-based and PDE-based algorithms. Furthermore, this study demonstrates the first application of in vivo EPT reconstruction at the ultra-high field of 5T.
Methods
A segment-constrained adaptive Savitzky-Golay (SG) differentiator was developed to improve Laplacian and gradient calculations. SG kernel sizes were optimized for specific tissue types based on segmentation, and kernel ranges were strictly confined within tissue boundaries. To further eliminate boundary effects, ill-conditioned voxels were identified using condition numbers of the SG fitting matrix and corrected using fitting results from stable neighboring voxels of the same tissue type. This differentiation strategy was applied to Phase-based (PB), Image-based (IB), and Generalized Image-based (GIB) methods. Additionally, for the GIB solver, a convection-diffusion model with spatially varying coefficients was implemented, assigning distinct parameters to boundary and non-boundary voxels. Improvements were validated against standard methods using 5T UTE and T1 data from eight healthy volunteers.
Results
Visual inspection demonstrated that artifacts and boundary blurring were significantly reduced across all three algorithms (PB, IB, and GIB) by the proposed framework compared to conventional methods. Enhanced delineation of fine tissue structures and improved homogeneity within tissues were observed. Quantitatively, the improved algorithms achieved higher Structural Similarity Index (SSIM) values relative to pseudo-reference maps (e.g., PB improved from 0.82±0.02 to 0.88±0.01), indicating superior structural fidelity and noise robustness.
Conclusion
Boundary artifacts in EPT are effectively mitigated by the proposed adaptive differentiation and spatially varying PDE constraint strategy. This framework enhances the reconstruction accuracy and visual quality of both simplified and advanced EPT models, facilitating high-precision conductivity mapping at ultra-high magnetic fields.