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Kinetic models are frequently used to quantify mechanisms for transfer and metabolism of radiotracers. These models are typically formulated in terms of differential equations for concentration time characteristics of the radioisotope. They make assumptions such as homogeneity of the tissue, which can be difficult to justify. A nonparametric analysis of the tissue residue is possible and this provides a novel approach to kinetic quantitation, which is not reliant on compartmental modelling assumptions. A comparison between the two methods (parametric and nonparametric) applied to data from 18F-Fluorodeoxyglucose (FDG) studies in subjects with gliomas and 15O-H2O (standard and extended parametric) in normals is presented. PET time-course data are extracted for a number of regions of interest, which include areas that are metabolically active, tumour tissues and normal healthy tissues. Time course data are modelled using the parametric approach utilizing nonlinear weighted least squares and using the nonparametric approach based on a piecewise constant residue. Improvements in fit are statistically evaluated by approximation with familiar F-distributions and by direct simulation. P-values for assessment of standard compartmental models are reported for a collection of regions FDG and 15O-H2O. The results of this analysis provide evidence against the use of standard compartmental models for analysis of typical region of interest data with these tracers.