What is the Lorentz sphere correction for the MRI measured field generated by tissue magnetic susceptibility: the spatial exclusivity of source and observer and the Cauchy principal value

The imaginary Lorentz sphere is used to calculate the tissue susceptibility induced field observed by water protons in MRI, which has led to unsettling discussions. Using spatial smoothing of microscopic quantities to derive macroscopic quantities, tissue is modeled as a continuous medium with steady electronic susceptibility sources and steady proton observers. The magnetic field is described as distribution. The electronic sources and proton observers have to be spatially separated to preserve the definition of susceptibility. This leads to the Cauchy principal value integration of the dipole kernel over tissue magnetization for calculating the susceptibility field, without referring the observer geometry.

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