Proof of linear MRI phase imaging from an internal fieldmap.

Area of Science:

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

Background:

• Brain MRI phase imaging relies on a linear spatial mapping assumption for internal fieldmaps, which lacks theoretical validation.
• The intravoxel spin precession dephasing mechanism is fundamental to MRI signal formation.

Purpose of the Study:

• To provide theoretical proof for the linear spatial mapping in brain MRI phase imaging.
• To introduce a novel approach by replacing the arithmetic mean with the geometric mean in MRI signal formation.

Main Methods:

• The study replaced the complex arithmetic mean of intravoxel dephasing isochromats with a complex geometric mean.
• Numerical T2*MRI simulations were conducted to compare arithmetic- and geometric-mean phase images under various conditions (spatial resolution, echo time, proton density weighting).

Main Results:

• The complex geometric mean model theoretically proves linear spatial mapping for MRI phase imaging without phase angle restrictions.
• Simulations showed high similarity between geometric and arithmetic means in small phase conditions (corr > 0.90 at TE < 10ms).
• Similarity decreased at larger phase angles (corr ≈ 0.80 at TE = 30ms, phase-wrapped).

Conclusions:

• Replacing the arithmetic mean with the geometric mean provides a theoretical proof for linear MRI phase imaging.
• This geometric mean approach validates linear spatial mapping beyond the small phase condition in spin precession angles.