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

Boheng Lin, Zizhuo Xie, Bo Zhang, Lin Wan, Ao Qiu, Qingguo Xie

TL;DR

This work addresses the lack of a theoretical baseline for how geometric sensitivity varies in the trans-axial plane of cylindrical PET systems. It derives a closed-form analytic model grounded in solid-angle geometry, defining the geometric sensitivity as $S_g = 1 - \\frac{\\Omega}{2\\pi}$ for the endcap configuration. The model is validated through GATE Monte Carlo simulations and physical experiments, revealing a counterintuitive trend: geometric sensitivity increases with trans-axial offset and peaks at the field-of-view boundary under finite-FOV conditions. As a geometry-only reference, the framework decouples geometric effects from detector properties, enabling clearer assessment of detector advances and informing protocol optimization, with future work planned to integrate detector efficiency and packing fraction via a more complete analytical sensitivity expression.

Abstract

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.

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

TL;DR

This work addresses the lack of a theoretical baseline for how geometric sensitivity varies in the trans-axial plane of cylindrical PET systems. It derives a closed-form analytic model grounded in solid-angle geometry, defining the geometric sensitivity as for the endcap configuration. The model is validated through GATE Monte Carlo simulations and physical experiments, revealing a counterintuitive trend: geometric sensitivity increases with trans-axial offset and peaks at the field-of-view boundary under finite-FOV conditions. As a geometry-only reference, the framework decouples geometric effects from detector properties, enabling clearer assessment of detector advances and informing protocol optimization, with future work planned to integrate detector efficiency and packing fraction via a more complete analytical sensitivity expression.

Abstract

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.

Paper Structure

This paper contains 17 sections, 24 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methods
  3. Analytical Model
  4. Definition of Sensitivity
  5. Geometric Modeling
  6. Computing Solid Angle
  7. Geometric Case Analysis
  8. Experiments and Simulations
  9. GATE Simulations
  10. Experiment
  11. Results
  12. Discussion and Future Work
  13. Conclusion
  14. Appendix: Computing Solid Angle
  15. Appendix: Case Analysis
  16. ...and 2 more sections

Figures (7)

  • Figure 1: Diagrams showing the PET cylindrical system within the defined spatial framework: (a) view sliced along the axial direction, and (b) view sliced along the trans-axial direction.
  • Figure 2: Plot of the geometric sensitivity as a function of trans-axial offset, calculated based on Equation \ref{['eq:Sg_line']}. The plot considers 100 evenly spaced points within $[0, R]$ for a PET system with dimensions $R = 405$ mm and $L = 153$ mm.
  • Figure 3: GATE simulated distributions of sensitivity with respect to trans-axial offset for FOV diameter of (a) 500 mm, (b) 600 mm, and (c) no FOV.
  • Figure 4: Experimental sensitivity w.r.t trans-axial offset. The effective FOV of the system was set to 500mm for this experiment.
  • Figure 5: Comparison of sensitivity as a function of trans-axial offset obtained from GATE simulations (left column), experimental measurements (middle column), and analytical predictions (right column).
  • ...and 2 more figures