Simple closed-form formulae to estimate near fields in living tissue layers due to dipole antenna exposure

Analysis of near electric and magnetic field magnitudes and pattern in tissue layers due to exposure from a dipole antenna would normally require extensive electromagnetic computation, with significant computing resource and time. In this paper, the authors have developed an analytical approach to provide a fast, intuitive estimate of near field exposure by direct closed-form formulae, without the need of integration by numerical computation. A computational tool based on the proposed approach has been developed in MATLAB^® to estimate near field exposure of various points of different tissue layers adjacent to a dipole operating in 900 MHz frequency. Results of this approach were obtained with significantly lower computational time when compared against those computed with a commercial Maxwell´s equations solver FEKO^®. Empirically-derived correction factors are introduced to adjust for the assumptions required in developing direct closed-form formulae. We found that the root mean square error in using the analytical formulae is less than 16.5% for considered scenarios, where we represent tissue layers with dielectric layers. The approach developed here is used to observe near fields at closer distance in comparison to previous literature, is capable to investigate fields at continuous resolution without requiring more computational resource, and has reconciled some discordant results in the literature.