Measuring gantry-gantry and gantry-table alignment in PET/CT

Inherent image registration of the PET and CT images is one of the key advantages of an integrated PET/CT scanner. This registration is predicated on understanding the relationship between the PET and CT gantry coordinates; rotational or translational misalignments of the PET and CT subsystems must either be eliminated by moving the gantries relative to one another or compensated for in the system's image formation algorithms. In addition, the alignment of the table to the PET and CT subsystems plays a key role in image registration, since the effect of table-gantry misalignment in CT images are different than the effect in PET images. This paper describes an algorithm to simultaneously measure the six degrees of freedom in gantry-gantry alignment (three rotations, three translations) plus the two important angular degrees of freedom for table alignment, based on common features identified in CT and PET phantom images. The coordinate transformation equations are linearized and the error between PET and CT feature locations is minimized by least squares; the result is a system of eight linear equations in eight unknowns. If the angular discrepancies are sufficiently large that the linear approximation loses its validity, the algorithm can be iterated to increase its accuracy.