Pharmacokinetic modeling of Gadolinium nanoparticles (Gd-NPs) with the sojourn time in vasa vasorum for the contrast enhanced MRI

Deposition of lipid in the artery wall called atherosclerosis is recognized as a major cause of cardiovascular disease that leads to death worldwide. A better understanding into factors that may influence the delivery of gadolinium nanoparticles (Gd-NPs) that enhances quality of magnetic resonance imaging in diagnosis may provide a vital key for atherosclerotic treatment. In this study, we propose a delay differential model for describing the dynamics of Gd-NPs in bloodstream, peripheral arteries, and vasa vasorum with two phenomena of Gd-NPs during a sojourn in vasa vasorum. We then investigate the dynamical behaviors of Gd-NPs and explore the effects of sojourn time and transfer rates of Gd-NPs on the concentration of Gd-NPs in vasa vasorum at the 12th hour after the administration of gadolinium chelates contrast media and also the maximum concentration of Gd-NPs in peripheral arteries and vasa vasorum. Our results suggest that the sojourn of Gd-NPs in vasa vasorum may lead to complex behaviors of Gd-NPs dynamics, and transfer rates of Gd-NPs may have a significant impact on the concentration of Gd-NPs.