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.

[1]  A M , ETHOD OF MEASURING THE RESISTIVITY AND HALL ' COEFFICIENT ON LAMELLAE OF ARBITRARY SHAPE , 2014 .

[2]  Dale C. Roberts,et al.  MRI Magnetic Field Stimulates Rotational Sensors of the Brain , 2011, Current Biology.

[3]  Robert Fettiplace,et al.  Prestin-Driven Cochlear Amplification Is Not Limited by the Outer Hair Cell Membrane Time Constant , 2011, Neuron.

[4]  Thomas A. Houpt,et al.  Circular swimming in mice after exposure to a high magnetic field , 2010, Physiology & Behavior.

[5]  I. Curthoys,et al.  The Configuration and Attachment of the Utricular and Saccular Maculae to the Temporal Bone , 2009, Annals of the New York Academy of Sciences.

[6]  R. Ciuman,et al.  Stria vascularis and vestibular dark cells: characterisation of main structures responsible for inner-ear homeostasis, and their pathophysiological relations , 2008, The Journal of Laryngology & Otology.

[7]  R. Bowtell,et al.  Magnetic‐field‐induced vertigo: A theoretical and experimental investigation , 2007, Bioelectromagnetics.

[8]  T. Yousry,et al.  Imaging anatomy of the vestibular and visual systems , 2007, Current opinion in neurology.

[9]  Y. Kurachi,et al.  Molecular and physiological bases of the K+ circulation in the mammalian inner ear. , 2006, Physiology.

[10]  G. Ziegelberger,et al.  International commission on non-ionizing radiation protection. , 2006, Progress in biophysics and molecular biology.

[11]  Dimitri Deserranno,et al.  Fluid-structural interactions in the inner ear , 2005 .

[12]  R Bowtell,et al.  Electric fields induced in a spherical volume conductor by temporally varying magnetic field gradients. , 2002, Physics in medicine and biology.

[13]  R Bowtell,et al.  Electric fields induced in a spherical volume conductor by temporally varying magnetic field gradients , 2002 .

[14]  A. Buizza,et al.  Convection, buoyancy or endolymph expansion: what is the actual mechanism responsible for the caloric response of semicircular canals? , 2002, Journal of vestibular research : equilibrium & orientation.

[15]  J. Herbertz.  Comment on the ICNIRP guidelines for limiting exposure to time-varying electric, magnetic, and electromagnetic fields (up to 300 GHz) , 1998, Health physics.

[16]  A. Ahlbom.  Guidelines for limiting exposure to time-varying electric, magnetic, and electromagnetic fields (up to 300 GHz) , 1998 .

[17]  Michael Griebel,et al.  Numerical Simulation in Fluid Dynamics: A Practical Introduction , 1997 .

[18]  K. Munro,et al.  The test-retest variability of the caloric test: a comparison of a modified air irrigation with the conventional water technique. , 1996, British journal of audiology.

[19]  Z. Zhang,et al.  A fast method to compute surface potentials generated by dipoles within multilayer anisotropic spheres. , 1995, Physics in medicine and biology.

[20]  J. Schenck,et al.  Health and Physiological Effects of Human Exposure to Whole‐Body Four‐Tesla Magnetic Fields during MRI , 1992, Annals of the New York Academy of Sciences.

[21]  Henk A. van der Vorst,et al.  Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems , 1992, SIAM J. Sci. Comput..

[22]  C M Oman,et al.  Dimensions of the horizontal semicircular duct, ampulla and utricle in the human. , 1987, Acta oto-laryngologica.

[23]  C M Oman,et al.  The influence of semicircular canal morphology on endolymph flow dynamics. An anatomically descriptive mathematical model. , 1987, Acta oto-laryngologica.

[24]  C M Oman,et al.  Dimensions of the horizontal semicircular duct, ampulla and utricle in the human. , 1987, Acta oto-laryngologica.

[25]  L R Young,et al.  The physiological range of pressure difference and cupula deflections in the human semicircular canal. Theoretical considerations. , 1972, Acta oto-laryngologica.

[26]  R. Kimura.  XLVIII Distribution, Structure, and Function of Dark Cells in the Vestibular Labyrinth , 1969, The Annals of otology, rhinology, and laryngology.

[27]  A. Coats,et al.  Body position and the intensity of caloric nystagmus. , 1967, Acta oto-laryngologica.

[28]  T CAWTHORNE,et al.  Temperature changes in the perilymph space in response to caloric stimulation in man. , 1954, Acta oto-laryngologica.