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This thesis describes different point based non-rigid registration methods in general and the "fast" radial basis functions (RBFs) non-rigid registration method in particular. We propose and implement three techniques for identifying features like points, curves and surfaces in medical images which represent displacement fields among such images and are later used in developing three corresponding fast and accurate non-rigid registration techniques. Each registration technique involves four main steps: feature extraction, correspondence between the features, RBF fitting to corresponding features, and evaluating the fitted method to the 3 D image data. The main goal of developing these three techniques is to see the effect of the increasing number of salient features in the form of anatomical point landmarks, curves and parameterised surfaces on the overall performance (speed and accuracy) of the tested registration algorithms. The point and curve based Fast RBF registration methods use manually placed anatomical point landmarks and principal curves, respectively. They ensure sub-second registration of standard-sized X-ray C'I' and MR datasets without loss of accuracy as compared to competing methods. However, both methods have limited performance in recovering large deformation due to small numbers of point landmarks. The surface based Fast RBF registration uses surface parameterisation and reparameterisation techniques as pre-processing steps to increase the number of point landmarks on a surface, establishing initial correspondences between points of a surface-pair using a minimum distortion based global surface parameterisation algorithm. Experimental results demonstrate target registration errors less than 2mm on intra-subject registration of various size 256/\3 MR real datasets. in conclusion, it is shown that the performance of the Fast RBF algorithm is less sensitive to the increasing number of point landmarks as compared to competing algorithms without substantial loss of accuracy.

Chapter One gives an overview of medical imaging techniques, focusing on and comparing the nuclear imaging techniques of single photon emission computed tomography (SPECT) and positron emission tomography (PET). The applications of copper radioisotopes in nuclear medicine are presented, in particular the development of copper bis(thiosemicarbazonate) complexes for use as hypoxia imaging agents. Hypoxia and current strategies for its diagnosis are also discussed. Chapter Two describes the introduction of a new linker to bis(thiosemicarbazone) ligands along with the subsequent synthesis and characterisation of the zinc(II) and copper(II) complexes. The functionalisation with a simple amino acid as a comparison with a different linker group is discussed, along with the radiolabelling with copper-64, in vitro and in vivo uptake experiments. The synthesis and characterisation of new ligands incorporating two linker groups is described, with the in vitro hypoxia uptake investigated Chapter Three presents a series of novel asymmetric ligands replacing one thione sulphur donor in the N2S2 bis(thiosemicarbazone) donor set with alternative donors. The synthesis and properties of the zinc(II), copper(II) and nickel(II) complexes are described and compared against those of the analogous bis(thiosemicarbazonate) complexes. The radiolabelling with copper-64 of these compounds is discussed as well as in vitro and in vivo uptake experiments. Chapter Four discusses the synthesis and characterisation of new compounds with further modifications to the bis(thiosemicarbazone) core structure. New groups are introduced to one of the ligands investigated in Chapter 3 to increase its functionality and some investigations with other radiochemically relevant metals are carried out. Symmetric N4 donor ligands and their complexes are also discussed along with preliminary investigations into N-methylated thiosemicarbazone ligands. Chapter Five describes the functionalisation of bis(thiosemicarbazone) ligands with fluorophores to allow the subcellular distribution of the copper(II) complex to be explored. The use of two photon fluorescence and fluorescence lifetime imaging microscopy (FLIM) to distinguish between the bis(thiosemicarbazone) ligand and copper(II) complex in vitro is discussed. Chapter Six gives a summary of the results described in Chapters Two to Five. Chapter Seven contains full experimental details of the work presented in this thesis.

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a tool that is used to measure tissue microvascular status by application of suitable tracer kinetic models. These are used to estimate parameters such as blood plasma volume (vp), endothelial permeability (Ktrans) and the size of the extravascular extracellular space (ve). Essential to DCE-MRI tracer kinetic analysis is the measurement of an arterial input function (AIF), which provides an estimate of the concentration of contrast agent in the blood plasma before it diffuses to the tissues. This measurement is challenging since potential sources of error lead to unreliable AIF characterisation and reduce the sensitivity with which DCE-MRI can detect physiological changes due to drug intervention. The aim of this work is to investigate and understand some of these sources of error and where possible to propose possible methodologies to reduce them.