A new discrete dipole kernel for quantitative susceptibility mapping.

Area of Science:

• Medical Imaging
• Magnetic Resonance Imaging (MRI)
• Computational Physics

Background:

• Quantitative susceptibility mapping (QSM) commonly uses continuous Fourier transform operators, which can lead to high-frequency aliasing errors.
• Existing QSM methods often rely on approximations in their forward models, impacting accuracy.

Purpose of the Study:

• To reduce aliasing errors in QSM by developing an alternative dipole kernel formulation.
• To investigate the impact of a discrete Fourier transform-based dipole kernel on QSM accuracy and image quality.

Main Methods:

• Developed and implemented a discrete dipole kernel formulation based on the discrete Fourier transform.
• Evaluated the discrete kernel's performance against the continuous formulation using synthetic phantoms and in vivo MRI data.
• Assessed forward model calculations and susceptibility inversion accuracy.

Main Results:

• The discrete kernel showed superior fits to analytic field solutions compared to the continuous kernel.
• Observed reduced over-oscillations and aliasing artifacts with the discrete kernel.
• Demonstrated error reduction and increased sharpness in QSM estimation.

Conclusions:

• Discretizing the dipole kernel offers advantages for QSM accuracy and image quality.
• The discrete kernel formulation is easily integrated into existing QSM software.
• Potential benefits for high-resolution QSM applications, especially with ultra-high field MRI, warrant further investigation.