Measurement and analysis of static magnetic fields that block action potentials in cultured neurons

To characterize the properties of static magnetic fields on firing of action potentials (AP) by sensory neurons in cell culture, we developed a mathematical formalism based on the expression for the magnetic field of a single circular current loop. The calculated fields fit closely the field measurements taken with a Hall effect gaussmeter. The biological effect induced by different arrays of permanent magnets depended principally on the spatial variation of the fields, quantified by the value of the gradient of the field magnitude. Magnetic arrays of different sizes (macroarray: four center-charged neodymium magnets of approximately 14 mm diameter; microarray; four micromagnets of the same material but of approximately 0.4 mm diameter) allowed comparison of fields with similar gradients but different intensities at the cell position. These two arrays had a common gradient value of approximately 1 mT/mm and blocked > 70% of AP. Alternatively, cells placed in a field strength of approximately 0.2 mT and a gradient of approximately 0.02 mT/mm produced by the macroarray resulted in no significant reduction of firing; a microarray field of the same strength but with a higher gradient of approximately 1.5 mT/mm caused approximately 80% AP blockade. The experimental threshold gradient and the calculated threshold field intensity for blockade of action potentials by these arrays were estimated to be approximately 0.02 mT/mm and approximately 0.02 mT, respectively, In conclusion, these findings suggest that spatial variation of the magnetic field is the principal cause of AP blockade in dorsal root ganglia in vitro.