Tomasi, Giampaolo (2007) Bayesian and population approaches for pixel-wise quantification of positron emission Tomography images: ridge regression and Global-Two-Stage. [Ph.D. thesis]
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PET (Positron Emission Tomography) is a technique in which a radioactive tracer which decays by positron emission is injected into the subject's body. Through a complex instrumentation and sophisticated reconstruction algorithms, it is then possible to compute the distribution of the tracer over time in the area of interest, which is the desired outcome of the measurement.
After reconstruction the image is ready for quantitative analysis, necessary to derive the so-called kinetic parameters, which are relevant in that they have a physiological meaning. This analysis may be performed either at ROI level (Region-Of-Interest, an anatomically homogeneous region such as cerebellum or thalamus) or at pixel level. In the latter scenario kinetic parameters are computed separately for each of the hundreds of thousand of pixels of the image, and the so-called parametric images are generated. Pixel-by-pixel analysis has the intrinsic problem due to the high noise level of pixel TACs (Time Activity Curve, i.e. the value of radioactive concentration as a function of time)
as this may give rise to unreliable estimates for the kinetic parameters or to non-convergence of the algorithms used for estimation. Parametric maps, however, are of paramount importance as they are characterized by a high spatial resolution: phenomena such as a lesion in a cerebral structure or the presence of a small tumoral mass may be invisible with ROI analysis but detectable even at simple visual inspection through pixel analysis.
The aim of this thesis was to develop fast methods for the generation of more reliable parametrci maps. A method already developed in literature, known as ridge regression (RR), was comprehensively studied and developed; in addition, a technique completely new to the field of PET , Global-Two-Stages(GTS), belonging to the field of population approaches , was proposed and tested. The basic ideas of these methodologies which make them part of the family of Bayesian approaches is, loosely speaking, to employ, in the parameter estimation for a given pixel, not only the TAC of that pixel but to incorporate also the information driving from the other pixels in order to obtain a global regularizing effect, penalizing, for instance the noisiest TACs..The analysis was carried out first on simulated data because, in order to be able to compute indices which quantify the goodness of final estimates such BIAS and Root Mean Square Error (RMSE), the knowledge of "true" parameters is necessary, and data are necessarily to be simulated. The performances of the proposed Bayesian algorithms were compared to those of the appropriate "gold standard" , the most used estimation method for the tracer under examination. Interest was then addressed to a real rich dataset of the tracer [11C]PK11195, very used for the study of pathologies such as Alzheimer and Huntington, in that it is linked to the overall level of neuroinflammation.
The analysis of simulated data revealed that RR and GTS gave always rise to decrease of RMSE, leving BIAS substantially unchanged.The improvements are clearly dependent on the tracer, nose level, and specific kinetic parameter considered.The study of the [11C]PK11195 dataset showed how RR and GTS much more regular parametric maps with respect to SRTM, the "gold standard" used for comparison. The proposed approaches (RR and GTS) also yielded excellent results in terms of the ability to differentiate between healthy and ill subjects on the basis of the maps of the kinetic parameter BP (Binding Potential): this fact has clearly a significant diagnostic impact as more reliable methods (i.e. with higher sensitivity and specificity) are needed for the daily application in clinical practise.
In conclusion, Ridge Regression and Global-Two-Stage are precious instruments for the improvement of parametric maps: both methodologies can be applied with virtually any tracer and model, provided that initial estimates can be computed through standard weighted least squares, and have therefore a wide range of applicability.
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