Electromagnetohydrodynamic modeling of Lorentz effect imaging.

Lorentz Effect Imaging (LEI) is an MRI technique that has been proposed for direct imaging of neuronal activity. While promising results have been obtained in phantoms and in the human median nerve in vivo, its contrast mechanism is still not fully understood. In this paper, computational model simulations were used to investigate how electromagnetohydrodynamics (EMHD) may explain the LEI contrast. Three computational models of an electrolyte-filled phantom subject to an applied current dipole, synchronized to oscillating magnetic field gradients of an LEI protocol, were developed to determine the velocity and displacement of water molecules as well as the resulting signal loss in an MR image. The simulated images were compared to images from previous LEI phantom experiments with identical properties for different stimulus current amplitudes and polarities. The first model, which evaluated ion trajectories based on Stokes flow using different mobility values, did not generate an appreciable signal loss due to an insufficient number of water molecules associated with the ion hydration shells. The second model, which computed particle drift based on the Lorentz force of charged particles in free space, was able to approximate the magnitude, but not the distribution of signal loss observed in the experimental images. The third model, which computed EMHD based on the Lorentz force and Navier-Stokes equations for flow of a conducting fluid, provided results consistent with both the magnitude and distribution of signal loss seen in the LEI experiments. Our EMHD model further yields information on electrical potential, velocity, displacement, and pressure, which are not readily available in an experiment, thereby providing a robust means to study and optimize LEI for imaging neuronal activity in the human cortex.