Displacement Patterns in Magnetomotive Ultrasound Explored by Finite Element Analysis

Magnetomotive ultrasound is an emerging technique that enables detection of magnetic nanoparticles. This has implications for ultrasound molecular imaging, and potentially addresses clinical needs regarding determination of metastatic infiltration of the lymphatic system. Contrast is achieved by a time-varying magnetic field that sets nanoparticle-laden regions in motion. This motion is governed by vector-valued mechanical and magnetic forces. Understanding how these forces contribute to observed displacement patterns is important for the interpretation of magnetomotive ultrasound images. Previous studies have captured motion adjacent to nanoparticle-laden regions that was attributed to diamagnetism. While diamagnetism could give rise to a force, it cannot fully account for the observed displacements in magnetomotive ultrasound. To isolate explanatory variables of the observed displacements, a finite element model is set up. Using this model, we explore potential causes of the unexplained motion by comparing numerical models with earlier experimental findings. The simulations reveal motion outside particle-laden regions that could be attributed to mechanical coupling and the principle of mass conservation. These factors produced a motion that counterbalanced the time-varying magnetic excitation, and whose extent and distribution was affected by boundary conditions as well as compressibility and stiffness of the surroundings. Our findings emphasize the importance of accounting for the vector-valued magnetic force in magnetomotive ultrasound imaging. In an axisymmetric geometry, that force can be represented by a simple scalar expression, an oversimplification that rapidly becomes inaccurate with distance from the symmetry axis. Additionally, it results in an underestimation of the vertical force component by up to 30%. We therefore recommend using the full vector-valued force to capture the magnetic interaction. This study enhances our understanding of how forces govern magnetic nanoparticle displacement in tissue, contributing to accurate analysis and interpretation of magnetomotive ultrasound imaging.