Dynamic contrast-enhanced MRI (DCE-MRI) is increasingly used to quantify and map the spatial distribution of blood-brain barrier (BBB) leakage in neurodegenerative disease, including cerebral small vessel disease and dementia. However, the subtle nature of leakage and resulting small signal changes make quantification challenging. While simplified one-dimensional simulations have probed the impact of noise, scanner drift, and model assumptions, the impact of spatio-temporal effects such as gross motion, k-space sampling and motion artefacts on parametric leakage maps has been overlooked. Moreover, evidence on which to base the design of imaging protocols is lacking due to practical difficulties and the lack of a reference method. To address these problems, we present an open-source computational model of the DCE-MRI acquisition process for generating four-dimensional Digital Reference Objects (DROs), using a high-resolution brain atlas and incorporating realistic patient motion, extra-cerebral signals, noise and k-space sampling. Simulations using the DROs demonstrated a dominant influence of spatio-temporal effects on both the visual appearance of parameter maps and on measured tissue leakage rates. The computational model permits a greater understanding of the sensitivity and limitations of subtle BBB leakage measurement and provides a non-invasive means of testing and optimising imaging protocols for future studies.