High-precision mapping of the magnetic field utilizing the harmonic function mean value property

Area of Science:

• Physics
• Medical Imaging
• Applied Mathematics

Background:

• Static magnetic field homogeneity is crucial for Magnetic Resonance Imaging (MRI).
• MR phase maps are sensitive to magnetic field inhomogeneities.
• Current phase mapping techniques have limitations in precision.

Purpose of the Study:

• To develop a novel method for enhancing the precision of MR phase and magnetic field mapping.
• To leverage the harmonic properties of static magnetic fields and MR phase maps.
• To demonstrate the method's effectiveness in phantoms and in vivo.

Main Methods:

• The study utilizes the property that static magnetic field components and MR phase maps are harmonic functions satisfying Laplace's equation.
• A mean value property for spherical surfaces is derived and experimentally validated.
• This property is applied to develop an improved phase and field mapping algorithm.

Main Results:

• The proposed method significantly improves the precision of MR phase and field mapping.
• Three-dimensional static magnetic field mapping with precision of 10(-11) to 10(-12) T was achieved in phantoms using a 1.5-T clinical scanner.
• This represents a three-orders-of-magnitude improvement over conventional methods.
• Successful in vivo application on human leg phase maps was demonstrated.

Conclusions:

• The derived mean value property offers a robust foundation for high-precision MR field mapping.
• The developed method substantially enhances accuracy in static magnetic field measurements.
• This technique holds promise for advanced MRI applications requiring precise field characterization.