Abstract
The spatial distributions of the static magnetic field components and MR phase maps in space with homogeneous magnetic susceptibility are shown to be harmonic functions satisfying Laplace's equation. A mean value property is derived and experimentally confirmed on phase maps: the mean value on a spherical surface in space is equal to the value at the center of the sphere. Based on this property, a method is implemented for significantly improving the precision of MR phase or field mapping. Three-dimensional mappings of the static magnetic field with a precision of 10(-11) approximately 10(-12) T are obtained in phantoms by a 1.5-T clinical MR scanner, with about three-orders-of-magnitude precision improvement over the conventional phase mapping technique. In vivo application of the method is also demonstrated on human leg phase maps.
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