Extracting detector energy non-linearity correction factors from a single Lu-176 background spectrum using an artificial neural network. (2020)

385 Introduction: Gamma ray detectors using silicon photomultipliers and time-over-threshold for energy measurement exhibit significant energy non-linearity. Correcting this non-linearity is important for achieving accurate energy information and sufficient energy resolution for gamma rays that deposit energy in multiple crystals through a combination of Compton scattering and photo-electric absorption. A typical method for calibrating the non-linearity involves making measurements with multiple isotopes to derive the spectral positions of multiple energies covering the range of intended use. Modern Positron Emission Tomography (PET) scanners often make use of gamma ray detectors using Lu-based scintillators. Lu-176 present in the scintillator provides a source of background radiation that can be used for calibration or daily quality control. Methods: In this work we present a method which uses an Artificial Neural Network (ANN) to extract non-linearity correction factors from a single Lu-176 background spectrum. This method requires no external radiation sources, it is extremely fast, and it provides better quantitative results than traditional least-squares fitting to a multi-parameter function. Our training data consist of Lu-176 background spectra (input) and multiple peak positions (target output) derived from separate measurements of several different radionuclides. Both input and target output data are in units of Time-over-Threshold (ToT). The data were divided into training, validation, and test sets. The ANN was trained to produce estimated positions for the peaks from the multiple individual isotopes. Training was terminated when the validation results stopped improving. The resulting peak positions were then fit to a 3-parameter function which was used to generate energy correction tables which are subsequently used to translate from ToT units to energy in keV. An ever-present challenge in developing PET calibration methods is that the currently-available observations might not cover the entire range of behavior that will be seen in future systems. To improve the robustness of the ANN to future changes in non-linearity coefficients that might result from manufacturing variations in the detector components or changes in operating parameters, we used a data augmentation technique to provide simulated training data with a wider range of non-linearity parameters than was originally present in our measured data. Results: One way to evaluate the results is to histogram the difference between the ANN output peak positions and the measured peak positions (target output), converted to keV using the three-parameter fit to the measured data. Evaluating only test data (i.e. data that was not used during training), for all of the multiple individual isotope peaks, the standard deviation between the ANN-estimated peak position and the measured peak position is less than 3 keV. Conclusions: The proposed method using an ANN to extract non-linearity correction factors from a single Lu-176 background spectrum is fast and convenient. Since the errors produced by the ANN are small compared to the typical energy resolution of detectors using Lu-based scintillators, we conclude that the proposed method provides sufficient accuracy for energy calibration of PET systems.