Effective digitized spatial size of unit dipole field in Quantitative Susceptibility Mapping

Quantitative Susceptibility Mapping (QSM) calculates a distribution of tissue magnetic susceptibility difference in vivo using measured magnetic field perturbation. The magnetic field perturbation can be approximated in first order by convolution of the susceptibility distribution with a spatial unit dipole field. Since the convolution has to be done in all space, a novel technique using harmonic properties of the dipole field is introduced to confine the calculation within the measurable region. However, discretized dipole field does not satisfy the harmonic property near its orign. Here, we investigate an effective spatial size of the dipole field in relation with the nonharmonic property using Shepp-Logan phantoms including partial volume effects. This study suggests that the dipole field can be effectively restricted to 15 voxels in diameter and that this value relates with the nonharmonic region of the discretized dipole field. Moreover, the effective size in a real space is scaled with a spatial resolution of a QSM experiment.