4D reconstruction of dynamic positron emission tomography (dPET) data suppresses noise in both the reconstructed image sequences and kinetic parameter estimates by fitting smooth temporal functions to the voxel time-activity-curves (TACs) during the reconstruction. Cancer imaging studies often have many tissues within the scanner field of view, leading to a wide range of TAC shapes to be fitted. The development of flexible temporal functions for use in such situations is an ongoing area of research, and forms the primary focus of this thesis. Two commonly used models for 4D-PET reconstruction in situations with diverse kinetics are the spectral model, which models TACs as weighted sums of convolutions of the arterial input function (AIF) with exponential decays, and spline functions. In a digital phantom study comparing the performance of 4D-PET reconstruction based on adaptive-knot cubic B-splines and the spectral model, the spline-based reconstruction produced the least biased images overall, though the spectral model based reconstruction provided a better bias-noise trade-off in the early time-frames. A spline-residue model describing TACs as weighted sums of convolutions of the AIF with cubic B-spline functions is then proposed. As with the spectral model, convolution with the AIF constrains the spline-residue model at early time-points, potentially enhancing noise suppression in early time-frames, while still allowing a wide range of TAC descriptions over the entire imaged time-course, thus limiting bias. In a digital phantom study comparing 4D-reconstructions based on the spline-residue model, adaptive-knot cubic B-splines, the spectral model and an irreversible two-tissue compartment model, spline-residue based 4D reconstruction produced the highest quality (lowest bias and noise) parametric maps of radiotracer uptake kinetics and was particularly effective at suppressing noise in the early time-frames. To investigate whether the proposed spline-reside model gives physiologically meaningful kinetic parameters, fits of the spline-residue model to FDG-dPET tumour TACs obtained from a dataset comprising 41 primary breast cancer patients, who also underwent tumour biopsies, are compared to fits of irreversible two- and three-tissue compartment models. These TACs were obtained from analytically reconstructed dPET images. Using goodness-of-fit measures, the spline-residue model was found to give the best description of the patient TACs, and after accounting for multiple hypothesis testing the flux constant from the spline-residue model produced the strongest correlations with gene expression data derived from the tumour biopsies.