Contrast agent enhanced magnetic resonance (MR) perfusion imaging provides an early, non-invasive indication of defects in the coronary circulation. However, the large variation of contrast agent properties, physiological state and imaging protocols means that optimisation of image acquisition is difficult to achieve. This situation motivates the development of a computational framework that, in turn, enables the efficient mapping of this parameter space to provide valuable information for optimisation of perfusion imaging in the clinical context. For this purpose a single-compartment porous medium model of capillary blood flow is developed which is coupled with a scalar transport model, to characterise the behaviour of both blood-pool and freely-diffusive contrast agents characterised by their ability to diffuse through the capillary wall into the extra-cellular space. A parameter space study is performed on the nondimensionalised equations using a 2D model for both healthy and diseased myocardium, examining the sensitivity of system behaviour to Peclet number, Damköhler number (Da), diffusivity ratio and fluid porosity. Assuming a linear MR signal response model, sample concentration time series data are calculated, and the sensitivity of clinically-relevant properties of these signals to the model parameters is quantified. Both upslope and peak values display significant non-monotonic behaviour with regard to the Damköhler number, with these properties showing a high degree of sensitivity in the parameter range relevant to contrast agents currently in use. However, the results suggest that signal upslope is the more robust and discerning metric for perfusion quantification, in particular for correlating with perfusion defect size. Finally, the results were examined in the context of nonlinear signal response, flow quantification via Fermi deconvolution and perfusion reserve index, which demonstrated that there is no single best set of contrast agent parameters, instead the contrast agents should be tailored to the specific imaging protocol and post-processing method to be used. 
A spatially-distributed computational model to quantify behaviour of contrast agents in MR perfusion imaging