4-D geometric sensitivity for multi-headed planar detector PET systems

A general formulation of the geometric sensitivity in the 4D projection domain is presented for multi-headed planar detector PET systems. It mainly has two components. The first defines the geometric sensitivity in the transverse plane. The second defines the geometric sensitivity in the axial direction. For continuous (or small stepping) rotating gantry, the geometric sensitivity is (or can be approximated as) independent of the projection angle, thus it is a 3D function of the projection bin, axial position and axial oblique angle. Generally speaking, the geometric sensitivity is coupled in the transverse plane and axial direction. A method is suggested to decouple these two factors with the cost of losing some partial data. The geometric sensitivity is further modeled with the effect of axial septa, and with the effect of crystal incident angle efficiency at stationary gantry. The theoretical calculation shows good agreement with the Monte Carlo simulation or real acquisition under three cases: rotating gantry with 3D imaging, rotating gantry with axial septa and stationary gantry with 3D imaging.