In general, this study is concerned with the development of theoretical basis for the use of magnetic nanoparticles (MNPs) for the needs of cardiology. A mathematical model reflecting the fundamental features of MNPs motion and transport in a liquid that flows in a channel modeling a stenotic blood vessel is introduced. The obtained results of computational simulations of MNPs transport revealed the presence of stagnant zones with vortices of the host liquid that appear near the stenosis. The application of a magnetic field to the channel provokes the accumulation of MNPs in these zones. An increased MNPs concentration near the stenosis makes it possible to determine the position and size of the stenosis using an external magnetic sensor. © 2023, The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature.