Theoretical development of a magnetic force and an induced motion in elastic media for a magneto-motive technique

The theoretical development of a magnetic force and an induced motion while applying a magnetic field to magnetic nanoparticles in elastic media is described. An analytical expression for tissue-surface displacement derived from Mindlin’s theory of elasticity in semi-infinite media was used to analyze the magneto-motive technique. The initial motion of the magnetic nanoparticles is driven by a constant magnetic force that displays a dampened transient motion before steady-state movement at twice the modulation frequency of the applied sinusoidal magnetic field. The motion of the nanoparticles at double the modulation frequency originated from the magnetic force being proportional to the product of the magnetic flux density and its gradient. Finally, we demonstrate the detection of iron-oxide nanoparticles taken up by liver parenchymal Kupffer cells and macrophages in atherosclerotic plaques by using a differential-phase optical coherence tomography (DP-OCT) system to compare simulation results with experimental data.