Image reconstruction for a multi-layer Compton telescope: an analytical model for three interaction events.

Area of Science:

• Nuclear Instrumentation and Methods
• Medical Physics
• Gamma-ray Imaging

Background:

• Compton Cameras are vital for detecting gamma rays in sub-MeV to MeV ranges, particularly for in vivo range verification in hadron therapy via prompt gamma detection.
• A key challenge is poor image quality when incident gamma-ray energy is unknown, motivating the development of multi-layer Compton Cameras.
• Three interaction events in multi-layer Compton Cameras offer enhanced spectral information for direct incident gamma-ray energy inference.

Purpose of the Study:

• To extend an existing spectral reconstruction algorithm for two interaction events to accommodate three interaction events in a three-layer Compton Telescope.
• To develop and validate analytical expressions for sensitivity and the System Matrix for three interaction events.
• To implement the new model within a List Mode Maximum Likelihood Expectation Maximization algorithm for four-dimensional image reconstruction.

Main Methods:

• Development of an analytical model for signal formation from three gamma-ray interactions.
• Derivation and validation of analytical expressions for sensitivity and System Matrix using Monte Carlo simulations.
• Implementation of the model in a List Mode Maximum Likelihood Expectation Maximization algorithm for image reconstruction.

Main Results:

• The proposed model successfully recovers the correct spectrum and spatial distribution of gamma-ray sources with ideal data.
• Monte Carlo studies identified incorrect interaction position estimation and missing energy from escaping secondaries as causes of image degradation with real data.
• Current experimental resolution and efficiency for three interaction events limit the recovery of complex radioactive source structures.

Conclusions:

• The developed model provides improved spectral information from three interaction events, promising enhanced image quality in Compton imaging.
• Future work will integrate this three-interaction event model with the existing two-interaction event model for simultaneous use.
• This integrated approach is expected to significantly improve the accuracy of in vivo range verification in hadron therapy.