For many MRI installations, the coil pattern that generates pulsed magnetic fields produced by gradient coils is not provided by the manufacturer. This has implications for accurate assessments of MRI worker exposures, which is currently an important topic of research. To correctly model the level of exposure, a full three-dimensional distribution of the magnetic field in the locality of the magnet end is required, which can be difficult to obtain by experimental measurements. This research presents one possible approach, in which the prediction of a current distribution that generates an approximately identical magnetic field profile is constrained by a small number of experimentally measured magnetic field sample points within a plane outside the gradient set. The presented methodology may take into consideration other important descriptors such as field uniformity in the imaging volume, gradient coil geometry/dimension, driving current, central field strength, etc. To exemplify the application of the proposed approach, the current density and matching magnetic field distributions of x-and z-axis gradient coils are approximated without preknowledge of the gradient coil patterns for a MRI system, followed by exposure evaluations of a tissue-equivalent numerical worker model in the vicinity of said gradients.