Feasibility study of the non-invasive estimation of the β+ arterial input function for human PET imaging

This work deals with the estimation of the concentration of molecules in arterial blood which are labelled with positron-emitting radioelements. This concentration is called 'β+ arterial input function'. This concentration has to be estimated for a large number of pharmacokinetic analyses. Nowadays it is measured through series of arterial sampling, which is an accurate method but requiring a stringent protocol. Complications might occur during arterial blood sampling because this method is invasive (hematomas, nosocomial infections). The objective of this work is to overcome this risk through a non-invasive estimation of β+ input function with an external detector and a collimator. This allows the reconstruction of blood vessels and thus the discrimination of arterial signal from signals in other tissues. Collimators in medical imaging are not adapted to estimate β+ input function because their sensitivity is very low. During this work, they are replaced by coded-aperture collimators, originally developed for astronomy. New methods where coded apertures are used with statistical reconstruction algorithms are presented. Techniques for analytical ray-tracing and for the acceleration of reconstructions are proposed. A new method which decomposes reconstructions on temporal sets and on spatial sets is also developed to efficiently estimate arterial input function from series of temporal acquisitions. This work demonstrates that the trade-off between sensitivity and spatial resolution in PET can be improved thanks to coded aperture collimators and statistical reconstruction algorithm; it also provides new tools to implement such improvements. (author)