Analytic Model of Trans-axial Sensitivity in Cylindrical PET Systems Based on Solid Angle

In positron emission tomography (PET), a clear theoretical model describing how system sensitivity varies as a source is moved trans-axially within the field of view (FOV) is lacking. The current understanding and practical intuition often suggest that sensitivity is maximum at the center of the FOV, an assumption reflected in standardized protocols. In this work, we derive an analytic model for the trans-axial-plane sensitivity distribution in a cylindrical PET scanner based on solid angle. The model, formulated as a function of trans-axial offset from the center, is validated through both Monte Carlo simulations and physical experiments on a representative system. We find that the derived theoretical distribution is essentially consistent with simulation and experimental results, revealing a non-intuitive feature: sensitivity increases with trans-axial offset, peaks at the edge of the FOV, and drops off sharply beyond it. This study provides the first closed-form model of trans-axial geometric sensitivity in cylindrical PET scanners, offering a vital benchmark for isolating detector technology improvements and revealing a non-intuitive, offset-dependent sensitivity profile that enables new protocol optimization strategies.