An analytical model for the calculation of the change in transmembrane potential produced by an ultrawideband electromagnetic pulse

The electric field pulse shape and change in transmembrane potential produced at various points within a sphere by an intense, ultrawideband pulse are calculated in a four stage, analytical procedure. Spheres of two sizes are used to represent the head of a human and the head of a rat. In the first stage, the pulse is decomposed into its Fourier components. In the second stage, Mie scattering analysis (MSA) is performed for a particular point in the sphere on each of the Fourier components, and the resulting electric field pulse shape is obtained for that point. In the third stage, the long wavelength approximation (LWA) is used to obtain the change in transmembrane potential in a cell at that point. In the final stage, an energy analysis is performed. These calculations are performed at 45 points within each sphere. Large electric fields and transmembrane potential changes on the order of a millivolt are produced within the brain, but on a time scale on the order of nanoseconds. The pulse shape within the brain differs considerably from that of the incident pulse. Comparison of the results for spheres of different sizes indicates that scaling of such pulses across species is complicated.