Abstract
Positron Emission Tomography (PET) is a radiotracer imaging technique based on the administration (typically by injection) of compounds labelled with positron emitting radionuclides to a patient under study. When the radio-isotope decays, it emits a positron, which travels a short distance before annihilating with an electron. This annihilation produces two high-energy (511 keV) gamma photons propagating in nearly opposite directions, along an imaginary line called Line of Response (LOR). In PET imaging, the photons emitted by the decaying isotope are detected with gamma cameras. These cameras consist of a lead collimator to ensure that all detected photons are propagated along parallel paths, a crystal scintillator to convert high-energy photons to visible light, photo-multiplier tubes (PMT) to transform light signals into electric signals, and associated electronics to determine the position of each incident photon from the light distribution in the crystal (Ollinger & Fessler, 1997). We have researched on how Artificial Neural Networks (henceforth ANNs or NNs) could be used for bias-corrected position estimation. Small-scale ANNs like the ones considered in this work can be easily implemented in hardware, due to their highly parallelizable structure. Therefore, we have tried to take advantage of the capabilities of ANNs for modelling the real detector response.
TopBackground
Traditionally, Anger logic (Anger, 1958) has been the most popular technique to obtain the the position of the centroid, or centre of the light distribution inside the scintillator crystal by means of a simple formula. The solution proposed by Anger involves connecting the PMT outputs to a simple resistor division circuit to obtain only four signals (X‾, X+, Y‾, Y+). However, Anger logic introduces some important drawbacks in the detection process: non-uniform spatial behaviour, differences between each PMT gain or the deformation of the light distribution when it approaches the edge of the scintillator. These problems are alleviated by using correction maps.
However, the presence of all these phenomena in traditional detectors still reduces the intrinsic resolution and produces non-uniform compression artifacts in the image and the so called border effects. The main consequence is an unavoidable reduction of the Useful Field Of View (UFOV) of the PET camera, which usually covers up to 60% of each crystal dimension.
With other methods such as Statistics Based Positioning (SBP) or Maximum Likelihood (ML) positioning, this UFOV can be increased to approximately the 80% of each dimension of the crystal, but these methods involve a heavier computational cost (Joung, Miyaoka, Kohlmyer & Lewellen 2001)(Chung, Choi, Song, Jung, Cho, Choe, Lee, Kim & Kim, 2004).
These drawbacks have not been fully overcome yet. Therefore, our proposal to introduce ANNs in the detection process as good quality estimators is well-grounded.
Some previous research has been made in this area for PMT (A.M. Bronstein, M.M. Bronstein, Zibulevsky & Zeevi, 2003) and Avalanche Photodiode (APD) based (Bruyndockx, Léonard, Tavernier, Lemaître & Devroede, 2004) detectors using neural networks. In this work, the detectors are based on continuous scintillators and Multi-Anode PMTs (MA-PMTs) employing charge division read-out circuits (Siegel, Silverman, Shao & Cherry, 1996).
Key Terms in this Chapter
Gamma Camera: A camera that detects gamma rays (often called Anger camera).
Depth Of Interaction (DOI): Depth inside the scintillator crystal where a photon interacts and produces a light distribution. Its 2D coordinates coincide with those of the incidence point for normal incidence but they differ slightly for oblique incidence. Therefore, its determination is vital for oblique incidence cases.
Anger Logic: A classic procedure to obtain the position of incidence of a photon on the scintillator crystal, which requires connecting the photomultiplier outputs to a resistive network to obtain only four outputs. With these signals, the position of the scintillation centroid is easily obtained using a simple formula. This method is acceptable in the central area of the crystal but it introduces a considerable error near its borders.
Useful Field of View (UFOV): Area of the scintillator crystal surface on which the incidence of gamma rays produces reasonable estimations of the position of incidence.
Multi-Layer Perceptron (MLP): A kind of feed-forward neural network which has at least one hidden layer of neurons.
Scintillator Crystal: When a particle interacts inside a scintillator cristal, it deposits energy. The scintitillator crystal re-emits part of that energy as photons in the visible spectrum. To allow this light to be measured from the outside, the crystal must also be transparent to that light. This is done by doping the crystal so that permitted states are created in the forbidden band of the material.
Neural Network: A network of many simple processors (“units” or “neurons”) that imitates a biological neural network. The units are connected by unidirectional communication channels, which carry numeric data. Neural networks can be trained to find nonlinear relationships in data, and are used in applications such as robotics, speech recognition, signal processing or medical diagnosis.
Discretized Positioning Circuit (DPC): An analog resistive network that receives a large amount of currents and “codes” them into a reduced number of them, introducing a minimum delay. These new currents are linear combinations of those generated by the photodetectors.
Positron Emission Tomography (PET): PET is a nuclear imaging technique based on the administration of radioactive substances (radiotracers), whose molecules have a radioactive isotope (radionuclide), to a patient under study, with the aim to trace some chemical or physiological process that takes place in the body, typically for diagnosis of heart diseases, cancer, etc. The images obtained in a PET system are 2D sections of the concentration distribution of a radiotracer inside the body. When joining these sections, a medical 3D image can be obtained.
Photomultiplier Tube (PMT): A part of the PET detector that receives the electromagnetic energy from the scintillator cristal and transforms that energy into electric pulses. This conversion is done in two stages: firstly the photons are absorbed, producing free electrons, and secondly a cascade amplification takes place.