Modelling FMRI motion artifacts using a simulated scanner

2 0 − = γ γ ρ where 0 M is the transverse magnetisation following the last RF excitation, ρ is the average spin density of this tissue type in this voxel, ) (t sc G is the applied gradient vector (in the scanner coordinate frame) at time t, and ) (t Bz is the field (along the z direction) at the origin, which can include any inhomogeneities. This integral can be evaluated analytically over the voxel giving