Statistical considerations in the kinetic analysis of PET-FDG brain tumour studies

Dynamic positron emission tomography (PET) imaging can be used to track the distribution of injected radio-labelled molecules over time in vivo. This is a powerful technique, which provides researchers and clinicians the opportunity to study the status of healthy and pathological tissue by examining how it processes substances of interest. Widely used tracers include 18F-uorodeoxyglucose, an analog of glucose, which is used as the radiotracer in over ninety percent of PET scans. This radiotracer provides a way of quantifying the distribution of glucose utilisation in vivo. The interpretation of PET time-course data is complicated because the measured signal is a combination of vascular delivery and tissue retention effects. If the arterial time-course is known, the tissue time-course can typically be expressed in terms of a linear convolution between the arterial time-course and the tissue residue function. As the residue represents the amount of tracer remaining in the tissue, this can be thought of as a survival function; these functions been examined in great detail by the statistics community. Kinetic analysis of PET data is concerned with estimation of the residue and associated functionals such as ow, ux and volume of distribution. This thesis presents a Markov chain formulation of blood tissue exchange and explores how this relates to established compartmental forms. A nonparametric approach to the estimation of the residue is examined and the improvement in this model relative to compartmental model is evaluated using simulations and cross-validation techniques. The reference distribution of the test statistics, generated in comparing the models, is also studied. We explore these models further with simulated studies and an FDG-PET dataset from subjects with gliomas, which has previously been analysed with compartmental modelling. We also consider the performance of a recently proposed mixture modelling technique in this study.

Narratives in early Irish law tracts

This thesis presents a study of the 112 narratives collected from the Corpus Iuris Hibernici. The selection of narratives is based on criteria informed by modern narratological theories. The significant presence of narratives in early Irish law tracts appears at odds with the normal conception of law texts as consisting solely of provisions, and therefore needs to be accounted for. Since no systematic study has been conducted of these legal narratives, this thesis serves as an introduction by giving firstly an index of narratives and secondly a categorisation of them in terms of distribution, dates and functions. It then carries out a general analysis of the relationship between legal narratives and early Irish literature, and a selected case study of the relationship between legal narratives and the legal institutions in the context of which the narratives are located. It has become clearer, with the progress of argument, that the use of narratives was an integral part of legal writing in medieval Ireland; and the narratives, though having many idiosyncratic features of themselves, are profoundly connected with the learned tradition at large. The legal narratives reveal the intellectual background and compositional concerns of medieval Irish jurists, and they formed a crucial part of the effort to accommodate law tracts into the dynamic tradition of senchas. Two appendices are included at the end: one consists of translations of 34 narratives from the index, and the other is a critical edition of one of the narratives discussed in detail, together with translations of some relevant passages.