Single Magnetic Particle Motion in Magnetomotive Ultrasound: An Analytical Model and Experimental Validation

Magnetomotive Ultrasound (MMUS) is an emerging imaging modality, in which magnetic nanoparticles (MNPs) are used as contrast agents. MNPs are driven by a time-varying magnetic force, and the resulting movement of the surrounding tissue is detected with a signal processing algorithm. However, there is currently no analytical model to quantitatively predict this magnetically-induced displacement. Toward the goal of predicting motion due to forces on the distribution of MNPs, in this work, a model originally derived from the Navier-Stokes equation for the motion of a single magnetic particle subject to a magnetic gradient force is presented and validated. Displacement amplitudes for a spatially inhomogeneous and temporally sinusoidal force were measured as a function of force amplitude and Young's modulus, and the predicted linear and inverse relationships were confirmed in gelatin phantoms, respectively, with three out of four data sets exhibiting R² ≥ 0.88 . The mean absolute uncertainty between the predicted displacement magnitude and experimental results was 14%. These findings provide a means by which the performance of MMUS systems may be predicted to verify that systems are working to theoretical limits and to compare results across laboratories.