Non-diverging analytical expression for the sensitivity of converging SPECT collimators

Area of Science:

• Medical Imaging Physics
• Nuclear Medicine Technology
• Instrumentation Science

Background:

• Accurate analytical expressions for collimator resolution and sensitivity are crucial for optimizing Single Photon Emission Computed Tomography (SPECT) systems.
• Existing sensitivity formulas for converging collimators often diverge near focal points or are limited to the collimator axis, restricting their use for certain geometries.

Purpose of the Study:

• To develop non-diverging analytical sensitivity formulas for astigmatic, cone beam, and fan beam collimators applicable across their full field-of-view.
• To enable the optimization of SPECT systems using converging collimators, particularly those with short focal lengths designed to focus within the object.

Main Methods:

• Derived non-diverging sensitivity formulas by integrating previously established collimator response functions over the entire detector surface.
• Fully accounted for the varying solid angle subtended by individual detector pixels, resulting in a closed-form, non-diverging expression.
• Validated the derived formulas using ray-tracing simulations for fan beam and astigmatic cone beam collimators.

Main Results:

• The new sensitivity formulas are non-diverging and applicable over the full field-of-view for various converging collimator types.
• Close agreement was found between the analytical expressions and ray-tracing simulations, with average differences less than 1% after accounting for septa placement variations.
• The derived expressions reduce to traditional diverging formulas under specific assumptions, confirming their validity.

Conclusions:

• The newly developed non-diverging sensitivity expressions enhance the ability to optimize SPECT collimators, especially for configurations with focal points near or within the object.
• These formulas address limitations of previous models, paving the way for improved sensitivity and resolution in advanced SPECT imaging applications.