In positron emission tomography (PET), coincidence detection of annihilation photons enables the measurement of Radon transforms of the instantaneous activity concentration of labelled tracers in the human body. Using reconstruction algorithms, spatial maps of the activity distribution can be created and analysed to reveal the pharmacokinetics of the labelled tracer. This thesis considers the possibility of applying pharmacokinetic modelling to the count rate data measured by the detectors, rather than reconstructed images, A new concept is proposed - parameter projections - Radon transforms of the spatial distribution of the parameters of the model, which simplifies the problem considerably. Using this idea, a general linear least squares GLLS framework is developed and applied to the one and two tissue-compartment models for [O-15]water and [F-18]FDG. Simulation models are developed from first principles to demonstrate the accuracy of the GLLS approach to parameter estimation. This requires the validation of the whole body distribution of each of the tracers, using pharmacokinetic techniques, leading to novel compartment based whole body models for [O-15]water and [F-18]FDG. A simplified Monte-Carlo framework for error estimation of the tissue models is developed, based on system parameters. It is also shown that the variances of maps of the spatial variance of the parameters of the model - parametric images - can be calculated in projection space. It is clearly demonstrated that the precision of the variance estimates is higher than that obtained from estimates based on reconstructed images. Using the methods, it is shown how statistical parametric maps of the difference between two neuronal activation conditions can be calculated from projection data. The methods developed allow faster results analysis, avoiding lengthy reconstruction of large data sets, and allow access to robust statistical techniques for activation analysis through use of the known, Poisson distributed nature, of the measured projection data.