Accuracy of the morphology enabled dipole inversion (MEDI) algorithm for quantitative susceptibility mapping in MRI

Area of Science:

• Medical Imaging
• Biophysics
• Computational Neuroscience

Background:

• Magnetic Resonance (MR) imaging is crucial for non-invasive brain analysis.
• Quantitative susceptibility mapping (QSM) aims to reconstruct magnetic susceptibility distributions from MR data.
• The inversion of the dipole kernel in QSM is an ill-posed inverse problem.

Purpose of the Study:

• To provide a rigorous mathematical demonstration of the accuracy of QSM algorithms, specifically morphology enabled dipole inversion (MEDI).
• To analyze the error bounds of the MEDI algorithm in QSM reconstruction.
• To validate the MEDI method's performance using numerical simulations and experimental data.

Main Methods:

• The study analyzes the error in QSM reconstructed by the MEDI algorithm.
• Error is expressed as a function of acquisition noise and spatial prior information error.
• Numerical analysis and phantom validation were employed to assess MEDI accuracy.

Main Results:

• The error in the susceptibility map reconstructed by MEDI is mathematically demonstrated to be bounded by a linear function of acquisition noise and spatial prior error.
• Numerical analysis shows MEDI reconstruction error is comparable to the noise level in the original MR data.
• Comprehensive edge detection in MEDI was found to reduce model error.

Conclusions:

• The MEDI algorithm provides a mathematically sound and experimentally validated approach for QSM.
• The error in MEDI-reconstructed susceptibility maps is predictable and influenced by noise and prior information quality.
• MEDI is a practical and accurate method for QSM in both phantom and human brain imaging.