Assessing the numerical accuracy of the impedance method.

The impedance method has been used extensively to calculate induced electric fields and currents in tissue as a result of applied electromagnetic fields. However, there has previously been no known method for an a priori assessment of the numerical accuracy of the results found by this method. Here, we present a method which permits an a priori assessment of the numerical accuracy of the impedance method applied to physiologically meaningful problems in bioengineering. The assessment method relies on estimating the condition number associated with the impedance matrix for problems with varying shapes, sizes, conductivities, anisotropies, and implementation strategies. Equations have been provided which predict the number of significant figures lost due to poor matrix conditioning as a function of these variables. The results show that, for problems of moderate size and uncomplicated geometry, applied fields should be measured or calculated accurately to at least five or six significant figures. As resolutions are increased and material properties are more widely divergent even more significant figures are needed. The equations provided here should ensure that solutions found from the impedance method are calculated accurately.

Differential activation of nerve fibers with magnetic stimulation in humans.

BACKGROUND: Earlier observations in our lab had indicated that large, time-varying magnetic fields could elicit action potentials that travel in only one direction in at least some of the myelinated axons in peripheral nerves. The objective of this study was to collect quantitative evidence for magnetically induced unidirectional action potentials in peripheral nerves of human subjects. A magnetic coil was maneuvered to a location on the upper arm where physical effects consistent with the creation of unidirectional action potentials were observed. Electromyographic (EMG) and somatosensory evoked potential (SEP) recordings were then made from a total of 20 subjects during stimulation with the magnetic coil. RESULTS: The relative amplitudes of the EMG and SEP signals changed oppositely when the current direction in the magnetic coil was reversed. This effect was consistent with current direction in the coil relative to the arm for all subjects. CONCLUSION: A differential evocation of motor and sensory fibers was demonstrated and indicates that it may be possible to induce unidirectional action potentials in myelinated peripheral nerve fibers with magnetic stimulation.

Differential activation and block of peripheral nerve fibers by magnetic fields.

The ability to noninvasively and reversibly block conduction in peripheral nerves would have several clinical applications. As an initial step in this direction, we investigated the possibility of magnetically generating and differentially blocking activity in mammalian peripheral nerve fibers in vitro. Compound action potentials at each end of individual explanted phrenic nerves were recorded in response to currents induced at the midpoint of the nerve with an externally placed magnetic coil. Current in the coil was then reversed and the recordings repeated. In all cases, the area under the compound action potential on the virtual anode side of the magnetic stimulus was reduced (mean of 18.2 +/- 8.8%) in comparison to the area on the virtual cathode side. This indicates that peripheral nerve activity can be differentially induced by magnetic stimulation. Extension of this effect to the point of generating unidirectional action potentials in vivo may prove clinically useful in a number of contexts, such as reducing contractures secondary to spasticity and generating magnetically induced anesthesia in limbs. Further investigations of this effect seem warranted.