A Fully Automated Method for Accurate Measurement of Geometrical Distortion in Magnetic Resonance Imaging of a 3D-Lattice Phantom

This paper describes an automated method for extracting the apparent positions of fiducial points from 2D or 3D images of a phantom. We consider a 3D-lattice phantom for two main reasons: first, ease of manufacture and isotropy of its structure with respect to coordinate projections; second, a connected structure allowing to uniquely assess the adjacency relationship between fiducial points even if geometric distortions arising from main magnet inhomogeneity and gradient fields non-linearity is severe as observed in open-bore systems. In order to validate our proposed method and compare different choices for the parameters of our phantom (i.e. number and distance between grids and thickness of its branches) we developed in-house a software for simulating 2D or 3D volume images of the phantom, using customizable MRI sequence parameters and Spherical Harmonic Coefficients for the fields. We deem worthy of note that using simulated images is the only way to evaluate the estimated position error, since it allows to compare the estimates to their theoretical counterparts. Furthermore, the use of simulated images allows to evaluate the robustness of the method with respect to image quality in terms of Signal-to-Noise Ratios and geometric distortion, and allows to evaluate different phantom geometries without having to manufacture them. The proposed method can be easily extended to phantoms having an arbitrary overall shape, as long as it is a fully connected structure. Specifically, it is easy to design a phantom with fiducial points laying outside of the homogeneity sphere, so that indirect measurement of the fields becomes possible, for example by using the recent method proposed by Acquaviva et al. To the best of our knowledge, the proposed method outperforms other state-of-the-art methods, with an average positioning offset of 0.052 mm (with a 0.99 quantile of 0.12 mm) when working on images featuring a differential Signal-to-Noise Ratio within Region-of-Interest (ROI) equal to 105 (20.2 dB) and a ROI-to-background SNR of 20 dB. Estimating the positions of 6859 fiducial points in a volume, our highest density case, was carried out in less than 30 minutes on a desktop personal computer.