isoPhasor: a generic and precise marker visualization, localization, and quantification method based on phase saddles in 3D MR imaging

Purpose: To derive a generic approach for accurate localization and characterization of susceptibility markers in MRI, compatible with many common types of pulse sequences, sampling trajectories, and acceleration methods. Theory and Methods: A susceptibility marker’s dipolar phase evolution creates 3 saddles in the phase gradient of the spatial encoding, for each sampled data point in k-space. The signal originating from these saddles can be focused at the location of the marker to create positive contrast. The required phase shift can be calculated from the scan parameters and the marker properties, providing a marker detection algorithm generic for different scan types. The method was validated numerically and experimentally for a broad range of spherical susceptibility markers (0.3 < radius < 1.6 mm, 10 < |∆χ| < 3300 ppm), under various conditions. Results: For all numerical and experimental phantoms, the average localization error was below one third of the voxel size, whereas the average error in magnetic strength quantification was 7%. The experiments included different pulse sequences (gradient echo, spin echo [SE], and free induction decay scans), sampling strategies (Cartesian, radial), and acceleration methods (echo planar imaging EPI, turbo SE). Conclusion: Spherical markers can be identified from their phase saddles, enabling clear visualization, precise localization, and accurate quantification of their magnetic strength, in a wide range of clinically relevant pulse sequences and sampling strategies.