Mechanical model of neural tissue displacement during Lorentz effect imaging

Abstract

Allen Song and coworkers recently proposed a method for MRI detection of biocurrents in nerves called "Lorentz effect imaging." When exposed to a magnetic field, neural currents are subjected to a Lorentz force that moves the nerve. If the displacement is large enough, an artifact is predicted in the MR signal. In this work, the displacement of a nerve of radius a in a surrounding tissue of radius b and shear modulus mu is analyzed. The nerve carries a current density J and lies in a magnetic field B. The solution to the resulting elasticity problem indicates that the nerve moves a distance BJ/4mu a2ln(b/a). Using realistic parameters for a human median nerve in a 4T field, this calculated displacement is 0.013 microm or less. The distribution of displacement is widespread throughout the tissue, and is not localized near the nerve. This displacement is orders of magnitude too small to be detected by conventional MRI methods.

Figure 1

A nerve of radius a lying in surrounding tissue of radius b. The magnetic field B is in the x direction. Current inside the nerve flows in the positive z direction (out of the paper), and current in the surrounding tissue flows in the negative z direction. The Lorentz force on the nerve is in the y direction, consistent with the "right-hand-rule."

Figure 2

The displacement produced by the Lorentz force, calculated using Eqs. 5, 10, and 12. a) The entire tissue. The outer circle has radius b and the inner circle radius a (b=25a) b) A detailed view of the displacement around the nerve. In the figure, the arrow length is exaggerated compared to the predicted displacement. The scale for the length of the arrows is set by the displacement at the center of the nerve, Eq. 22.