Dynamic O-15 labelled water ([15O]H2O)-positron emission tomography (PET) and dynamic contrast-enhanced (DCE) magnetic resonance imaging (MRI) in conjunction with pharmacokinetic modelling have been widely used in research in order to quantify cerebral perfusion as well as other physiological parameters that could help us understand tissue function and assess drug delivery. However, the two modalities have been used independently and potential benefits from a joint analysis in order to acquire complementary information have not yet been investigated. This is the main purpose of the thesis with the technique applied in high-grade glioma which is one of the most challenging tissues to be studied as it is characterised by high heterogeneity, spans a wide range of perfusion values and confronts the underlying assumptions made in both modalities when performing pharmacokinetic analysis. The two modalities were first independently investigated in order to assess their noise characteristics, model performance in the tissue of interest and potentially improve spatial resolution before combining them. A method to assess model performance and estimate parameter precision using chi-square statistics while incorporating in its estimation the non uniform noise distribution in the DCE-MR images is proposed. A model with two exponentials was found to describe the data significantly better in the glioma region compared to models with a single exponential and a long acquisition was needed to increase parameter precision. A method of anisotropic filtering is also proposed in order to reduce noise in the DCE-MR images and substantially increase parameter precision. For dynamic [15O]H2O-PET, an alternative method of reconstruction was used (complementary frame reconstruction) which in combination with resolution modelling and an 15O resolution kernel improved accuracy in a phantom experiment and contrast in clinical data for both radioactivity concentration images and parametric maps of perfusion. Finally, a model with two compartments and a voxel input function instead of an arterial input function is proposed for joint analysis in tumour. The voxel input function increased accuracy of the parameter estimates in the superior sagittal sinus for the DCE-MRI data while joint analysis enabled estimation of perfusion without having to make any underlying assumptions (i.e. negligible blood volume) and estimation of permeability and extraction of the MR contrast agent.