Quantitative pharmacokinetic analysis of Positron Emission Tomography (PET) data typically requires a dynamic scan of at least one hour, which poses a challenge for both clinical and research studies. Instead, in standard practice, a static 10 minute scan is used to calculate the standardised uptake value ratio (SUVR). SUVR approximates tracer binding but is biased by blood flow changes, rendering it unsuitable for longitudinal studies. In this thesis, the availability of magnetic resonance imaging (MRI) data, simultaneously acquired from a PET-MR scanner is exploited to reduce the time required for accurate PET quantification. The main body of this work comprises the development of a framework to incorporate blood flow information from arterial spin labelled (ASL) MRI data into the existing simplified reference tissue model (SRTM) to replace the early phase of the PET data, reducing the acquisition time. This reduced acquisition time (RT-) SRTM was evaluated on [18F]-florbetapir data for the estimation of both regional average and voxelwise amyloid burden (BPND), and was validated against the gold standard BPND using a 60 minute scan. The first step of the RT-SRTM requires the PET tracer delivery parameter, R1, to be estimated from the ASL cerebral blood flow (CBF) maps. Several methods were evaluated: linear regression using region as a covariate, multi-atlas propagation with image fusion, and deep learning based regression using a convolutional neural network. The RT-SRTM was shown to facilitate accurate regional voxelwise quantification in half the acquisition time (30 minutes). Additionally, deep learning based regression was used to learn the model which maps ASL-CBF and dynamic PET data to BPND in a single step (SSDL). The SS-DL model exploits all available information, and avoids noise sensitive voxelwise fitting. This allows the acquisition time to be cut to 15 minutes, and facilitates accurate voxelwise BPND quantification on a timescale manageable for almost all patients and studies.