• PET
• positron range
• iterative reconstruction algorithm

Positron Emission tomography (PET) is a nuclear medical imaging technique which allows non-invasive quantitative assessment of biochemical and functional processes. Its purpose is to determine the distribution of radioactive tracers, chosen depending on the tissues and organs of interest, inside the patient body.

The principle at the base of PET image production is the detection (achieved by the use of scintillation detectors) of the two photons generated by electron-positron annihilation. The annihilation photons are emitted at 180° to each other and therefore permit to localize their source along a straight line of coincidence without the need for physical collimation.
PET data consist in detected coincidence events between pairs of detectors and, since it is assumed that the tracer concentration is stationary, the reconstruction problem can be summarized in recovering it from the acquired data, that correspond to the radiotracer projections.

There are two main approaches for dealing with PET data: one is to assume that PET data are deterministic and that it is therefore possible to find the exact solution for the image (analytical algorithms), the other is to take account of the intrinsically stochastic nature of the projection data, leading to estimation techniques that tend to approximate solutions (iterative algorithms).

This thesis deals with iterative reconstruction algorithms and aims at taking into account the positron range effect, since positron range in tissue is one of the most important physical limitation to spatial resolution in PET scanners. Before annihilation the positron travels a finite distance interacting with the surrounding medium, thus the photon-producing event occurs outside the radioactive nucleus and the actual position of the radiotracer, that we wish to determine, does not lie on the line defined by the two photons, i.e. the line of response (LOR). Since in the reconstruction process it is assumed that the radiotracer lies on the LOR, the positron range results in a blurring that affects the image quality.

In this thesis, in order to study the trend of the positron range annihilation distribution on varying the isotope and the tissue, simulations have been performed using GATE (Geant4 Application for Tomographic Emission), that is a Monte Carlo simulator very commonly used by the PET community. Various isotope-medium combinations have been simulated and positron end point coordinates have been analyzed.

A method is then proposed to account for positron range blurring in image reconstruction: by means of specific kernel representing the annihilation density probability, a blurring can be added on the object during the forward projection.
The blurring kernel is a three dimensional matrix whose dimensions, in terms of number of voxels, depend on the isotope-medium combination, on the size of the image voxel and on user defined cut-offs. The blurring is achieved through a convolution of the image and the kernel performed by
centering the flipped kernel at each voxel in the image and computing the inner product between voxel values in the image and voxel values in the kernel.

In this thesis the kernel values are calculated in two different ways: they have been directly obtained from Monte Carlo simulations, from which annihilations coordinates can be easily extracted and then voxelized (fully Monte Carlo kernel), or using analytical functions that fit the experimental three-dimensional annihilation probability density function (analytical kernel).

These two kinds of kernel are evaluated for four positron emitting isotopes frequently used in PET imaging (Fluorine-18, Oxygen-15, Gallium-68 and Rubidium-82), considering their behaviour in water. Finally, to evaluate the result of the filtering process, images of real and simulated acquisitions of a pre-clinical PET scanner, reconstructed with and without the positron range blurring, are compared. A comparison is also made between the performances of the two different kinds of blurring kernel.