Magnetic field effects on the vestibular system: calculation of the pressure on the cupula due to ionic current-induced Lorentz force.

Large static magnetic fields may be employed in magnetic resonance imaging (MRI). At high magnetic field strengths (usually from about 3 T and above) it is possible for humans to perceive a number of effects. One such effect is mild vertigo. Recently, Roberts et al (2011 Current Biology 21 1635-40) proposed a Lorentz-force mechanism resulting from the ionic currents occurring naturally in the endolymph of the vestibular system. In the present work a more detailed calculation of the forces and resulting pressures in the vestibular system is carried out using a numerical model. Firstly, realistic 3D finite element conductivity and fluid maps of the utricle and a single semi-circular canal containing the current sources (dark cells) and sinks (hair cells) of the utricle and ampulla were constructed. Secondly, the electrical current densities in the fluid are calculated. Thirdly, the developed Lorentz force is used directly in the Navier-Stokes equation and the trans-cupular pressure is computed. Since the driving force field is relatively large in comparison with the advective acceleration, we demonstrate that it is possible to perform an approximation in the Navier-Stokes equations that reduces the problem to solving a simpler Poisson equation. This simplification allows rapid and easy calculation for many different directions of applied magnetic field. At 7 T a maximum cupula pressure difference of 1.6 mPa was calculated for the combined ampullar (0.7 µA) and utricular (3.31 µA) distributed current sources, assuming a hair-cell resting current of 100 pA per unit. These pressure values are up to an order of magnitude lower than those proposed by Roberts et al using a simplistic model and calculation, and are in good agreement with the estimated pressure values for nystagmus velocities in caloric experiments. This modeling work supports the hypothesis that the Lorentz force mechanism is a significant contributor to the perception of magnetic field induced vertigo.